We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if and only if a certain 1-form is exact and a certain function vanishes (this function automatically vanishes for linear constraints). Moreover, this result can be extended to geodesic flows for arbitrary metric connections and the sufficient condition manifests as integrability of the torsion. As a consequence, volume-preservation of a nonholonomic system is closely related to the torsion of the nonholonomic connection. Examples of nonlinear/affine/linear constraints are considered.
{"title":"Existence of invariant volumes in nonholonomic systems subject to nonlinear constraints","authors":"W. Clark, A. Bloch","doi":"10.3934/jgm.2023011","DOIUrl":"https://doi.org/10.3934/jgm.2023011","url":null,"abstract":"We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if and only if a certain 1-form is exact and a certain function vanishes (this function automatically vanishes for linear constraints). Moreover, this result can be extended to geodesic flows for arbitrary metric connections and the sufficient condition manifests as integrability of the torsion. As a consequence, volume-preservation of a nonholonomic system is closely related to the torsion of the nonholonomic connection. Examples of nonlinear/affine/linear constraints are considered.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81177146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work we introduce a category $LDP_d$ of discrete-time dynamical systems, that we call discrete Lagrange--D'Alembert--Poincare systems, and study some of its elementary properties. Examples of objects of $LDP_d$ are nonholonomic discrete mechanical systems as well as their lagrangian reductions and, also, discrete Lagrange-Poincare systems. We also introduce a notion of symmetry group for objects of $LDP_d$ and a process of reduction when symmetries are present. This reduction process extends the reduction process of discrete Lagrange--Poincare systems as well as the one defined for nonholonomic discrete mechanical systems. In addition, we prove that, under some conditions, the two-stage reduction process (first by a closed and normal subgroup of the symmetry group and, then, by the residual symmetry group) produces a system that is isomorphic in $LDP_d$ to the system obtained by a one-stage reduction by the full symmetry group.
{"title":"Lagrangian reduction of nonholonomic discrete mechanical systems by stages","authors":"Javier Fernandez, Cora Tori, M. Zuccalli","doi":"10.3934/jgm.2020029","DOIUrl":"https://doi.org/10.3934/jgm.2020029","url":null,"abstract":"In this work we introduce a category $LDP_d$ of discrete-time dynamical systems, that we call discrete Lagrange--D'Alembert--Poincare systems, and study some of its elementary properties. Examples of objects of $LDP_d$ are nonholonomic discrete mechanical systems as well as their lagrangian reductions and, also, discrete Lagrange-Poincare systems. We also introduce a notion of symmetry group for objects of $LDP_d$ and a process of reduction when symmetries are present. This reduction process extends the reduction process of discrete Lagrange--Poincare systems as well as the one defined for nonholonomic discrete mechanical systems. In addition, we prove that, under some conditions, the two-stage reduction process (first by a closed and normal subgroup of the symmetry group and, then, by the residual symmetry group) produces a system that is isomorphic in $LDP_d$ to the system obtained by a one-stage reduction by the full symmetry group.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79040771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Normal modes are intimately related to the quadratic approximation of a potential at its hyperbolic equilibria. Here we extend the notion to the case where the Taylor expansion for the potential at a critical point starts with higher order terms, and show that such an extension shares some of the properties of standard normal modes. Some symmetric examples are considered in detail.
{"title":"Higher order normal modes","authors":"G. Gaeta, S. Walcher","doi":"10.3934/jgm.2020026","DOIUrl":"https://doi.org/10.3934/jgm.2020026","url":null,"abstract":"Normal modes are intimately related to the quadratic approximation of a potential at its hyperbolic equilibria. Here we extend the notion to the case where the Taylor expansion for the potential at a critical point starts with higher order terms, and show that such an extension shares some of the properties of standard normal modes. Some symmetric examples are considered in detail.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80191320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, first we introduce the notion of a $ mathsf{VB} $-Lie $ 2 $-algebroid, which can be viewed as the categorification of a $ mathsf{VB} $-Lie algebroid. The tangent prolongation of a Lie $ 2 $-algebroid is a $ mathsf{VB} $-Lie $ 2 $-algebroid naturally. We show that after choosing a splitting, there is a one-to-one correspondence between $ mathsf{VB} $-Lie $ 2 $-algebroids and flat superconnections of a Lie 2-algebroid on a 3-term complex of vector bundles. Then we introduce the notion of a $ mathsf{VB} $-$ mathsf{CLWX} $ 2-algebroid, which can be viewed as the categorification of a $ mathsf{VB} $-Courant algebroid. We show that there is a one-to-one correspondence between split Lie 3-algebroids and split $ mathsf{VB} $-$ mathsf{CLWX} $ 2-algebroids. Finally, we introduce the notion of an $ E $-$ mathsf{CLWX} $ 2-algebroid and show that associated to a $ mathsf{VB} $-$ mathsf{CLWX} $ 2-algebroid, there is an $ E $-$ mathsf{CLWX} $ 2-algebroid structure on the graded fat bundle naturally. By this result, we give a construction of a new Lie 3-algebra from a given Lie 3-algebra, which provides interesting examples of Lie 3-algebras including the higher analogue of the string Lie 2-algebra.
{"title":"Categorification of $ mathsf{VB} $-Lie algebroids and $ mathsf{VB} $-Courant algebroids","authors":"Y. Sheng","doi":"10.3934/jgm.2023002","DOIUrl":"https://doi.org/10.3934/jgm.2023002","url":null,"abstract":"In this paper, first we introduce the notion of a $ mathsf{VB} $-Lie $ 2 $-algebroid, which can be viewed as the categorification of a $ mathsf{VB} $-Lie algebroid. The tangent prolongation of a Lie $ 2 $-algebroid is a $ mathsf{VB} $-Lie $ 2 $-algebroid naturally. We show that after choosing a splitting, there is a one-to-one correspondence between $ mathsf{VB} $-Lie $ 2 $-algebroids and flat superconnections of a Lie 2-algebroid on a 3-term complex of vector bundles. Then we introduce the notion of a $ mathsf{VB} $-$ mathsf{CLWX} $ 2-algebroid, which can be viewed as the categorification of a $ mathsf{VB} $-Courant algebroid. We show that there is a one-to-one correspondence between split Lie 3-algebroids and split $ mathsf{VB} $-$ mathsf{CLWX} $ 2-algebroids. Finally, we introduce the notion of an $ E $-$ mathsf{CLWX} $ 2-algebroid and show that associated to a $ mathsf{VB} $-$ mathsf{CLWX} $ 2-algebroid, there is an $ E $-$ mathsf{CLWX} $ 2-algebroid structure on the graded fat bundle naturally. By this result, we give a construction of a new Lie 3-algebra from a given Lie 3-algebra, which provides interesting examples of Lie 3-algebras including the higher analogue of the string Lie 2-algebra.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88753780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The connection between the dynamics in relative periodic orbits of vector fields with noncompact symmetry groups and periodic control for the class of control systems on Lie groups known as '(robotic) locomotion systems' is well known, and has led to the identification of (geometric) phases. We take an approach which is complementary to the existing ones, advocating the relevance——for trajectory generation in these control systems——of the qualitative properties of the dynamics in relative periodic orbits. There are two particularly important features. One is that motions in relative periodic orbits of noncompact groups can only be of two types: either they are quasi-periodic, or they leave any compact set as begin{document}$ ttopminfty $end{document} ('drifting motions'). Moreover, in a given group, one of the two behaviours may be predominant. The second is that motions in a relative periodic orbit exhibit 'spiralling', 'meandering' behaviours, which are routinely detected in numerical integrations. Since a quantitative description of meandering behaviours for drifting motions appears to be missing, we provide it here for a class of Lie groups that includes those of interest in locomotion (semidirect products of a compact group and a normal vector space). We illustrate these ideas on some examples (a kinematic car robot, a planar swimmer).
The connection between the dynamics in relative periodic orbits of vector fields with noncompact symmetry groups and periodic control for the class of control systems on Lie groups known as '(robotic) locomotion systems' is well known, and has led to the identification of (geometric) phases. We take an approach which is complementary to the existing ones, advocating the relevance——for trajectory generation in these control systems——of the qualitative properties of the dynamics in relative periodic orbits. There are two particularly important features. One is that motions in relative periodic orbits of noncompact groups can only be of two types: either they are quasi-periodic, or they leave any compact set as begin{document}$ ttopminfty $end{document} ('drifting motions'). Moreover, in a given group, one of the two behaviours may be predominant. The second is that motions in a relative periodic orbit exhibit 'spiralling', 'meandering' behaviours, which are routinely detected in numerical integrations. Since a quantitative description of meandering behaviours for drifting motions appears to be missing, we provide it here for a class of Lie groups that includes those of interest in locomotion (semidirect products of a compact group and a normal vector space). We illustrate these ideas on some examples (a kinematic car robot, a planar swimmer).
{"title":"Control of locomotion systems and dynamics in relative periodic orbits","authors":"F. Fassò, S. Passarella, M. Zoppello","doi":"10.3934/jgm.2020022","DOIUrl":"https://doi.org/10.3934/jgm.2020022","url":null,"abstract":"The connection between the dynamics in relative periodic orbits of vector fields with noncompact symmetry groups and periodic control for the class of control systems on Lie groups known as '(robotic) locomotion systems' is well known, and has led to the identification of (geometric) phases. We take an approach which is complementary to the existing ones, advocating the relevance——for trajectory generation in these control systems——of the qualitative properties of the dynamics in relative periodic orbits. There are two particularly important features. One is that motions in relative periodic orbits of noncompact groups can only be of two types: either they are quasi-periodic, or they leave any compact set as begin{document}$ ttopminfty $end{document} ('drifting motions'). Moreover, in a given group, one of the two behaviours may be predominant. The second is that motions in a relative periodic orbit exhibit 'spiralling', 'meandering' behaviours, which are routinely detected in numerical integrations. Since a quantitative description of meandering behaviours for drifting motions appears to be missing, we provide it here for a class of Lie groups that includes those of interest in locomotion (semidirect products of a compact group and a normal vector space). We illustrate these ideas on some examples (a kinematic car robot, a planar swimmer).","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89388600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We perform Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express both of the (Lie-Poisson) systems as couplings of two of their textit{mutually interacting} (Lie-Poisson) subdynamics. Mutually acting systems are beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address textit{matched pair Lie-Poisson} formulation permitting mutual interactions. Then, all mutual actions, as well as dual and induced cross-actions, are clearly computed for the kinetic moments and the Vlasov plasma. For both cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the higher-order ($geq 2$) kinetic moments. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma and, obtain the matched pair decomposition of this realization as well.
{"title":"Matched pair analysis of the Vlasov plasma","authors":"Ougul Esen, S. Sutlu","doi":"10.3934/JGM.2021011","DOIUrl":"https://doi.org/10.3934/JGM.2021011","url":null,"abstract":"We perform Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express both of the (Lie-Poisson) systems as couplings of two of their textit{mutually interacting} (Lie-Poisson) subdynamics. Mutually acting systems are beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address textit{matched pair Lie-Poisson} formulation permitting mutual interactions. Then, all mutual actions, as well as dual and induced cross-actions, are clearly computed for the kinetic moments and the Vlasov plasma. For both cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the higher-order ($geq 2$) kinetic moments. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma and, obtain the matched pair decomposition of this realization as well.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82923916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L. Colombo, Mar'ia Emma Eyrea Iraz'u, E. G. Andr'es
This note discusses Routh reduction for hybrid time-dependent mechanical systems. We give general conditions on whether it is possible to reduce by symmetries a hybrid time-dependent Lagrangian system extending and unifying previous results for continuous-time systems. We illustrate the applicability of the method using the example of a billiard with moving walls.
{"title":"A note on Hybrid Routh reduction for time-dependent Lagrangian systems","authors":"L. Colombo, Mar'ia Emma Eyrea Iraz'u, E. G. Andr'es","doi":"10.3934/jgm.2020014","DOIUrl":"https://doi.org/10.3934/jgm.2020014","url":null,"abstract":"This note discusses Routh reduction for hybrid time-dependent mechanical systems. We give general conditions on whether it is possible to reduce by symmetries a hybrid time-dependent Lagrangian system extending and unifying previous results for continuous-time systems. We illustrate the applicability of the method using the example of a billiard with moving walls.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78443929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we show that the spaces of sections of the $n$-th differential operator bundle $dev^n E$ and the $n$-th skew-symmetric jet bundle $jet_n E$ of a vector bundle $E$ are isomorphic to the spaces of linear $n$-vector fields and linear $n$-forms on $E^*$ respectively. Consequently, the $n$-omni-Lie algebroid $dev Eoplusjet_n E$ introduced by Bi-Vitagliago-Zhang can be explained as certain linearization, which we call pseudo-linearization of the higher analogue of Courant algebroids $TE^*oplus wedge^nT^*E^*$. On the other hand, we show that the omni $n$-Lie algebroid $dev Eoplus wedge^njet E$ can also be explained as certain linearization, which we call Weinstein-linearization of the higher analogue of Courant algebroids $TE^*oplus wedge^nT^*E^*$. We also show that $n$-Lie algebroids, local $n$-Lie algebras and Nambu-Jacobi structures can be characterized as integrable subbundles of omni $n$-Lie algebroids.
本文证明了向量束$E$的$n$-微分算子束$dev^n E$和$n$-偏对称射流束$jet_n E$的截面空间分别同构于$E^*$上的线性$n$-向量场和线性$n$-形式的空间。因此，Bi-Vitagliago-Zhang引入的$n$- omnii - lie代数群$dev Eoplusjet_n E$可以解释为Courant代数群$TE^*oplus wedge^nT^*E^*$的伪线性化。另一方面，我们证明了全n-李代数元E dev Eo + wedge^njet E$也可以被解释为一定的线性化，我们称之为Courant代数元的高级类似物TE^*o + wedge^nT^*E^*$的温斯坦线性化。我们还证明了$n$-李代数、局部$n$-李代数和Nambu-Jacobi结构可以被表征为全$n$-李代数的可积子束。
{"title":"Linearization of the higher analogue of Courant algebroids","authors":"H. Lang, Y. Sheng","doi":"10.3934/jgm.2020025","DOIUrl":"https://doi.org/10.3934/jgm.2020025","url":null,"abstract":"In this paper, we show that the spaces of sections of the $n$-th differential operator bundle $dev^n E$ and the $n$-th skew-symmetric jet bundle $jet_n E$ of a vector bundle $E$ are isomorphic to the spaces of linear $n$-vector fields and linear $n$-forms on $E^*$ respectively. Consequently, the $n$-omni-Lie algebroid $dev Eoplusjet_n E$ introduced by Bi-Vitagliago-Zhang can be explained as certain linearization, which we call pseudo-linearization of the higher analogue of Courant algebroids $TE^*oplus wedge^nT^*E^*$. On the other hand, we show that the omni $n$-Lie algebroid $dev Eoplus wedge^njet E$ can also be explained as certain linearization, which we call Weinstein-linearization of the higher analogue of Courant algebroids $TE^*oplus wedge^nT^*E^*$. We also show that $n$-Lie algebroids, local $n$-Lie algebras and Nambu-Jacobi structures can be characterized as integrable subbundles of omni $n$-Lie algebroids.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76509645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
James Montaldi's expertises span many areas on pure and applied mathematics. I will discuss here just one, his contributions to the motion of point vortices, specially the role of symmetries in the bifurcations and stability of equilibrium configurations in surfaces of constant curvature. This approach leads, for instance, to a very elegant proof of a classical result, the nonlinear stability of Thompson's regular heptagon in the plane. Here the plane appears "in passing", just as the transition between positive and negative curvatures.
{"title":"Getting into the vortex: On the contributions of james montaldi","authors":"J. Koiller","doi":"10.3934/jgm.2020018","DOIUrl":"https://doi.org/10.3934/jgm.2020018","url":null,"abstract":"James Montaldi's expertises span many areas on pure and applied mathematics. I will discuss here just one, his contributions to the motion of point vortices, specially the role of symmetries in the bifurcations and stability of equilibrium configurations in surfaces of constant curvature. This approach leads, for instance, to a very elegant proof of a classical result, the nonlinear stability of Thompson's regular heptagon in the plane. Here the plane appears \"in passing\", just as the transition between positive and negative curvatures.","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75957297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In August 2018 we held a conference in Guanajuato, Mexico, where several collaborators and students of James Montaldi had the privilege to homage his scientific contributions. James is best known as an expert in singularity and bifurcation theory, who is a world reference in equivariant Hamiltonian systems, and has an exceptional talent to turn symmetries into insightful theorems about the dynamics of mechanical systems. His unusual combination of mathematical depth, modesty, integrity and friendly personality, make him a greatly esteemed member of the extended geometric mechanics community. The programme of this exciting meeting, which lasted one week, incorporated some of the many areas in which James has worked over the years. During the conference, we heard testimonials of James’ mathematical sharpness, kindness and generosity as a supervisor and collaborator, accompanied with many nostalgic references of a meeting that he organised in Peyresq twenty years ago. This issue of the Journal of Geometric Mechanics is a continuation of our celebration of James’ career and of our appreciation of having him as a teacher, colleague and friend. Out of the many topics of the conference, the following two allow us to better understand his background and expertise, and to describe a noteworthy contribution to symmetric Hamiltonian systems that he made at an early stage of his career:
{"title":"Preface to the special issue dedicated to James Montaldi","authors":"L. García-Naranjo, M. León, J. Ortega","doi":"10.3934/jgm.2020028","DOIUrl":"https://doi.org/10.3934/jgm.2020028","url":null,"abstract":"In August 2018 we held a conference in Guanajuato, Mexico, where several collaborators and students of James Montaldi had the privilege to homage his scientific contributions. James is best known as an expert in singularity and bifurcation theory, who is a world reference in equivariant Hamiltonian systems, and has an exceptional talent to turn symmetries into insightful theorems about the dynamics of mechanical systems. His unusual combination of mathematical depth, modesty, integrity and friendly personality, make him a greatly esteemed member of the extended geometric mechanics community. The programme of this exciting meeting, which lasted one week, incorporated some of the many areas in which James has worked over the years. During the conference, we heard testimonials of James’ mathematical sharpness, kindness and generosity as a supervisor and collaborator, accompanied with many nostalgic references of a meeting that he organised in Peyresq twenty years ago. This issue of the Journal of Geometric Mechanics is a continuation of our celebration of James’ career and of our appreciation of having him as a teacher, colleague and friend. Out of the many topics of the conference, the following two allow us to better understand his background and expertise, and to describe a noteworthy contribution to symmetric Hamiltonian systems that he made at an early stage of his career:","PeriodicalId":49161,"journal":{"name":"Journal of Geometric Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86768001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：