Pub Date : 2022-05-31DOI: 10.1080/14689367.2023.2230917
Houssam Boukhecham
We prove that a $C^1$ hyperbolic map whose differential is regular enough has an SRB measure. The precise regularity condition is weaker than H{"o}lder and was mentionned by various authors through the developement of expanding and uniformly hyperbolic dynamics.
{"title":"Existence of SRB measures for hyperbolic maps with weak regularity","authors":"Houssam Boukhecham","doi":"10.1080/14689367.2023.2230917","DOIUrl":"https://doi.org/10.1080/14689367.2023.2230917","url":null,"abstract":"We prove that a $C^1$ hyperbolic map whose differential is regular enough has an SRB measure. The precise regularity condition is weaker than H{\"o}lder and was mentionned by various authors through the developement of expanding and uniformly hyperbolic dynamics.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42317155","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}
Pub Date : 2022-05-30DOI: 10.1080/14689367.2022.2083485
Dengdi Chen, Yan Zheng
The current paper is devoted to 3D stochastic Ginzburg–Landau equations with degenerate random forcing. We establish the stability of stochastic systems by investigating the relationship between invariant measures under the action of transition semigroups corresponding to different sets of parameters. Towards this aim a new form of bound on the difference between solutions along with the spectral gap plays a significant role.
{"title":"Stability of the invariant measure for the 3D stochastic cubic Ginzburg–Landau systems","authors":"Dengdi Chen, Yan Zheng","doi":"10.1080/14689367.2022.2083485","DOIUrl":"https://doi.org/10.1080/14689367.2022.2083485","url":null,"abstract":"The current paper is devoted to 3D stochastic Ginzburg–Landau equations with degenerate random forcing. We establish the stability of stochastic systems by investigating the relationship between invariant measures under the action of transition semigroups corresponding to different sets of parameters. Towards this aim a new form of bound on the difference between solutions along with the spectral gap plays a significant role.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"554 - 563"},"PeriodicalIF":0.5,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49619388","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}
Pub Date : 2022-05-24DOI: 10.1080/14689367.2022.2078686
Diego S. Ledesma, Robert Andres Galeano Anaya, Fabiano Borges da Silva
Consider a compact submanifold N without the boundary of a Riemannian manifold M, and a stochastic flow associated with a stochastic differential equation. Let be the random compact submanifold obtained by the action of the stochastic flow. In this work, we present an Itô formula for the volume of the random variable and, as a main result, we obtain estimates for its average growth assuming that Ricci curvature is bounded. We first analyse the particular case where the submanifolds are closed curves, thus obtaining estimates for the arc length, and then we study the volume variation of compact submanifolds of dimensions greater than or equal to 2. In addition, we apply our results to the special case where the vector fields of stochastic differential equation are conformal Killing.
{"title":"Estimates for the volume variation of compact submanifolds driven by a stochastic flow","authors":"Diego S. Ledesma, Robert Andres Galeano Anaya, Fabiano Borges da Silva","doi":"10.1080/14689367.2022.2078686","DOIUrl":"https://doi.org/10.1080/14689367.2022.2078686","url":null,"abstract":"Consider a compact submanifold N without the boundary of a Riemannian manifold M, and a stochastic flow associated with a stochastic differential equation. Let be the random compact submanifold obtained by the action of the stochastic flow. In this work, we present an Itô formula for the volume of the random variable and, as a main result, we obtain estimates for its average growth assuming that Ricci curvature is bounded. We first analyse the particular case where the submanifolds are closed curves, thus obtaining estimates for the arc length, and then we study the volume variation of compact submanifolds of dimensions greater than or equal to 2. In addition, we apply our results to the special case where the vector fields of stochastic differential equation are conformal Killing.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"527 - 553"},"PeriodicalIF":0.5,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41341546","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 first characterize the minimality criterion for a convergent power series f on in terms of its coefficients for the cases p = 2 or 3. For an arbitrary prime , the minimality criterion of such a series can be obtained explicitly provided that the prescribed minimal conditions for the reduction of f modulo p are found. Second, we provide the minimality criterion for a rational map of at least degree 2 with good reduction on the projective line over . This criterion enables us to obtain a complete description of minimal conditions for such a map on in terms of its coefficients for p = 2 or 3. For an arbitrary prime , we present a method of characterizing minimal rational maps ϕ of degree on , provided that the prescribed conditions for the reduction of ϕ on to be transitive are known.
{"title":"Minimality criteria for convergent power series over Z p and rational maps with good reduction on the projective line over Q p","authors":"Sangtae Jeong, Dohyun Ko, Yongjae Kwon, Youngwoo Kwon","doi":"10.1080/14689367.2022.2073870","DOIUrl":"https://doi.org/10.1080/14689367.2022.2073870","url":null,"abstract":"In this paper, we first characterize the minimality criterion for a convergent power series f on in terms of its coefficients for the cases p = 2 or 3. For an arbitrary prime , the minimality criterion of such a series can be obtained explicitly provided that the prescribed minimal conditions for the reduction of f modulo p are found. Second, we provide the minimality criterion for a rational map of at least degree 2 with good reduction on the projective line over . This criterion enables us to obtain a complete description of minimal conditions for such a map on in terms of its coefficients for p = 2 or 3. For an arbitrary prime , we present a method of characterizing minimal rational maps ϕ of degree on , provided that the prescribed conditions for the reduction of ϕ on to be transitive are known.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"493 - 526"},"PeriodicalIF":0.5,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42283299","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}
Pub Date : 2022-05-12DOI: 10.1080/14689367.2022.2072710
Nguyen Duong Toan
In this paper, we consider the longtime behaviour for the strongly damped wave equation with time-dependent memory kernels on a bounded domain . The main novelty of our result is that the memory kernel depends on time, allowing to describe the dynamics of aging materials. We first investigate the existence and uniqueness of weak solutions and then, we obtain the existence of the time-dependent global attractors in . We also prove the regularity of the time-dependent global attractor , i.e. is bounded in , with a bound independent of t. Finally, when approaches a multiple of the Dirac mass at zero as , we prove that the asymptotic dynamics of our problem is close to the one of its formal limit describing viscoelastic solids of Kelvin–Voigt type.
{"title":"Time-dependent global attractors for strongly damped wave equations with time-dependent memory kernels","authors":"Nguyen Duong Toan","doi":"10.1080/14689367.2022.2072710","DOIUrl":"https://doi.org/10.1080/14689367.2022.2072710","url":null,"abstract":"In this paper, we consider the longtime behaviour for the strongly damped wave equation with time-dependent memory kernels on a bounded domain . The main novelty of our result is that the memory kernel depends on time, allowing to describe the dynamics of aging materials. We first investigate the existence and uniqueness of weak solutions and then, we obtain the existence of the time-dependent global attractors in . We also prove the regularity of the time-dependent global attractor , i.e. is bounded in , with a bound independent of t. Finally, when approaches a multiple of the Dirac mass at zero as , we prove that the asymptotic dynamics of our problem is close to the one of its formal limit describing viscoelastic solids of Kelvin–Voigt type.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"466 - 492"},"PeriodicalIF":0.5,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44251494","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}
Pub Date : 2022-05-12DOI: 10.1080/14689367.2022.2071234
Mei-Chun Wei, Yongxiang Li
In this paper, based on the monotone iterative technique and the operator semigroup theory, a class of nonlocal problem of structural damped elastic systems with delay is studied in the case of noncompact semigroups in ordered Banach space. First, on the premise of the existence of upper and lower mild solutions, the existence and uniqueness of mild solutions for the elastic system are obtained. Then, an existence theorem of positive mild solutions for elastic system is obtained without assuming lower and upper mild solutions. Finally, as the application of abstract results, the existence and uniqueness of mild solutions and positive mild solutions for two classes of nonlocal damped beam vibration equations with delay are discussed.
{"title":"Monotone iterative technique for nonlocal problems of damped elastic systems with delay","authors":"Mei-Chun Wei, Yongxiang Li","doi":"10.1080/14689367.2022.2071234","DOIUrl":"https://doi.org/10.1080/14689367.2022.2071234","url":null,"abstract":"In this paper, based on the monotone iterative technique and the operator semigroup theory, a class of nonlocal problem of structural damped elastic systems with delay is studied in the case of noncompact semigroups in ordered Banach space. First, on the premise of the existence of upper and lower mild solutions, the existence and uniqueness of mild solutions for the elastic system are obtained. Then, an existence theorem of positive mild solutions for elastic system is obtained without assuming lower and upper mild solutions. Finally, as the application of abstract results, the existence and uniqueness of mild solutions and positive mild solutions for two classes of nonlocal damped beam vibration equations with delay are discussed.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"444 - 465"},"PeriodicalIF":0.5,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46173945","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}
Pub Date : 2022-05-09DOI: 10.1080/14689367.2022.2122779
C. Buzzi, Yagor Romano Carvalho, J. Llibre
These last years an increasing interest appeared in studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. The understanding of the dynamics of these systems has many difficulties. One of them is the study of their limit cycles. In this paper, we study the maximum number of crossing limit cycles of some classes of planar discontinuous piecewise differential systems separated by a straight line and formed by combinations of linear centres (consequently isochronous) and cubic isochronous centres with homogeneous nonlinearities. For these classes of planar discontinuous piecewise differential systems we solved the extension of the 16th Hilbert problem, i.e. we provide an upper bound for their maximum number of crossing limit cycles.
{"title":"Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres","authors":"C. Buzzi, Yagor Romano Carvalho, J. Llibre","doi":"10.1080/14689367.2022.2122779","DOIUrl":"https://doi.org/10.1080/14689367.2022.2122779","url":null,"abstract":"These last years an increasing interest appeared in studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. The understanding of the dynamics of these systems has many difficulties. One of them is the study of their limit cycles. In this paper, we study the maximum number of crossing limit cycles of some classes of planar discontinuous piecewise differential systems separated by a straight line and formed by combinations of linear centres (consequently isochronous) and cubic isochronous centres with homogeneous nonlinearities. For these classes of planar discontinuous piecewise differential systems we solved the extension of the 16th Hilbert problem, i.e. we provide an upper bound for their maximum number of crossing limit cycles.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"710 - 728"},"PeriodicalIF":0.5,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46210044","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}
Pub Date : 2022-04-21DOI: 10.1080/14689367.2022.2066508
J. Llibre, C. Valls
The new Euler–Jacobi formula for points with multiplicity two provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have eight finite singular points, being one of them with multiplicity two. The case with nine finite singular points has already been solved using the classical Euler–Jacobi formula.
{"title":"The improved Euler–Jacobi formula and the planar cubic polynomial vector fields in ℝ2","authors":"J. Llibre, C. Valls","doi":"10.1080/14689367.2022.2066508","DOIUrl":"https://doi.org/10.1080/14689367.2022.2066508","url":null,"abstract":"The new Euler–Jacobi formula for points with multiplicity two provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have eight finite singular points, being one of them with multiplicity two. The case with nine finite singular points has already been solved using the classical Euler–Jacobi formula.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"403 - 443"},"PeriodicalIF":0.5,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44962195","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}
Pub Date : 2022-04-04DOI: 10.1080/14689367.2022.2060066
J. Shu, Lu Zhang, Xin Huang, Jian Zhang
This paper is concerned with the well-posedness as well as long-term dynamics of stochastic Ginzburg–Landau equations driven by nonlinear noise. We will apply a specific method to solve stochastic Ginzburg–Landau equations, known as the variational approach. We prove the existence and uniqueness of the solutions by assuming that the coefficients satisfy certain monotonicity assumptions. The mean random dynamical system generated by the solution operators is proved to possess a unique weak pullback mean random attractor in a Bochner space. At the same time, the existence of invariant measures for the stochastic Ginzburg–Landau equations is also established.
{"title":"Dynamics of stochastic Ginzburg–Landau equations driven by nonlinear noise","authors":"J. Shu, Lu Zhang, Xin Huang, Jian Zhang","doi":"10.1080/14689367.2022.2060066","DOIUrl":"https://doi.org/10.1080/14689367.2022.2060066","url":null,"abstract":"This paper is concerned with the well-posedness as well as long-term dynamics of stochastic Ginzburg–Landau equations driven by nonlinear noise. We will apply a specific method to solve stochastic Ginzburg–Landau equations, known as the variational approach. We prove the existence and uniqueness of the solutions by assuming that the coefficients satisfy certain monotonicity assumptions. The mean random dynamical system generated by the solution operators is proved to possess a unique weak pullback mean random attractor in a Bochner space. At the same time, the existence of invariant measures for the stochastic Ginzburg–Landau equations is also established.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"382 - 402"},"PeriodicalIF":0.5,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48060021","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}
Pub Date : 2022-04-01DOI: 10.1080/14689367.2023.2170213
M. Barczy
We show an elementary way to calculate the exact Lyapunov exponent of affine Boole transformations using the interchangeability theorem for differentiation and integration due to Leibniz.
{"title":"On calculation of the exact Lyapunov exponent of affine Boole transformations","authors":"M. Barczy","doi":"10.1080/14689367.2023.2170213","DOIUrl":"https://doi.org/10.1080/14689367.2023.2170213","url":null,"abstract":"We show an elementary way to calculate the exact Lyapunov exponent of affine Boole transformations using the interchangeability theorem for differentiation and integration due to Leibniz.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"38 1","pages":"236 - 248"},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46735020","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：