Pub Date : 2018-01-02DOI: 10.1080/1726037X.2017.1417725
Chatuphol Khaofong, P. Kumam, Parinya Sa Ngiamsumthorn, J. Martínez-Moreno
Abstract In this work, we will introduce the new classes of product spaces and also establish the existence of coincidence points in quasi-ordered fuzzy metric spaces. In order to investigate the integral equations and ordinary differential equations is solutions of the systems. Also study the property of mixed-monotone and comparable property of quasi-ordered fuzzy metric spaces in the product space. Our theorems improve and cover the corresponding recent results announced by Wu (2014) and Roldan et al. (2014).
{"title":"Some coincidence point results in the product space for solutions of the fuzzy of ordinary differential equations and integral equations systems","authors":"Chatuphol Khaofong, P. Kumam, Parinya Sa Ngiamsumthorn, J. Martínez-Moreno","doi":"10.1080/1726037X.2017.1417725","DOIUrl":"https://doi.org/10.1080/1726037X.2017.1417725","url":null,"abstract":"Abstract In this work, we will introduce the new classes of product spaces and also establish the existence of coincidence points in quasi-ordered fuzzy metric spaces. In order to investigate the integral equations and ordinary differential equations is solutions of the systems. Also study the property of mixed-monotone and comparable property of quasi-ordered fuzzy metric spaces in the product space. Our theorems improve and cover the corresponding recent results announced by Wu (2014) and Roldan et al. (2014).","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"55 - 88"},"PeriodicalIF":0.9,"publicationDate":"2018-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2017.1417725","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42828607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-01-02DOI: 10.1080/1726037X.2017.1413063
Buşra Aktaş, Olgun Durmaz, Halit Gündoğan
Abstract Rodrigues parameters depend on the tangent of the half rotation angle in Euclidean space but in Dual space, dual Rodrigues parameters contain both rotation angle and distance corresponding the shortest distance between the straight lines in ℝ3. In this paper, we give Cayley's formula for the dual hyperbolic spherical motion and explain 3×3 type L-Dual skew symmetric matrices by using properties of this formula. Then, we obtain Rodrigues parameters of dual Hyperbolic unit sphere and show that Rodrigues parameters contain the hyperbolic rotation angle which is being between timelike lines and distance which is the minimal Lorentzian distance between the timelike lines of .
{"title":"Rodrigues parameters on dual hyperbolic unit sphere","authors":"Buşra Aktaş, Olgun Durmaz, Halit Gündoğan","doi":"10.1080/1726037X.2017.1413063","DOIUrl":"https://doi.org/10.1080/1726037X.2017.1413063","url":null,"abstract":"Abstract Rodrigues parameters depend on the tangent of the half rotation angle in Euclidean space but in Dual space, dual Rodrigues parameters contain both rotation angle and distance corresponding the shortest distance between the straight lines in ℝ3. In this paper, we give Cayley's formula for the dual hyperbolic spherical motion and explain 3×3 type L-Dual skew symmetric matrices by using properties of this formula. Then, we obtain Rodrigues parameters of dual Hyperbolic unit sphere and show that Rodrigues parameters contain the hyperbolic rotation angle which is being between timelike lines and distance which is the minimal Lorentzian distance between the timelike lines of .","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"1 - 16"},"PeriodicalIF":0.9,"publicationDate":"2018-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2017.1413063","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44940638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-01-02DOI: 10.1080/1726037X.2018.1436269
S. Merati, M. R. Farhangdoost
Abstract In this work, we present definition of the representation of double Lie algebroids and find a one-to-one correspondence to introduce representation up to homotopy of double Lie algebroids and gauge equivalence of them. Also dual, tensor product and direct sum representations up to homotopy are made as a double Lie algebroid modules. We conclude this paper by generalization of some Lie algebroid oo-representation properties to oo-representation of double Lie algebroids and introduce transgression classes for double Lie algebroids.
{"title":"Representation up to homotopy of double algebroids and their transgression classes","authors":"S. Merati, M. R. Farhangdoost","doi":"10.1080/1726037X.2018.1436269","DOIUrl":"https://doi.org/10.1080/1726037X.2018.1436269","url":null,"abstract":"Abstract In this work, we present definition of the representation of double Lie algebroids and find a one-to-one correspondence to introduce representation up to homotopy of double Lie algebroids and gauge equivalence of them. Also dual, tensor product and direct sum representations up to homotopy are made as a double Lie algebroid modules. We conclude this paper by generalization of some Lie algebroid oo-representation properties to oo-representation of double Lie algebroids and introduce transgression classes for double Lie algebroids.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"89 - 99"},"PeriodicalIF":0.9,"publicationDate":"2018-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2018.1436269","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41354324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-01-02DOI: 10.1080/1726037X.2017.1413065
M. Saidani, B. Belaïdi
ABSTRACT In this paper, we investigate the growth and value distribution of meromorphic solutions to higher order homogeneous and nonhomogeneous linear differential equations in which the coefficients are entire functions of finite [p, q]-order. We get the results about [p, q]-order and the [p, q]-convergence exponent of solutions for such equations.
{"title":"Meromorphic solutions to linear differential equations with entire coefficients of [p,q]-order","authors":"M. Saidani, B. Belaïdi","doi":"10.1080/1726037X.2017.1413065","DOIUrl":"https://doi.org/10.1080/1726037X.2017.1413065","url":null,"abstract":"ABSTRACT In this paper, we investigate the growth and value distribution of meromorphic solutions to higher order homogeneous and nonhomogeneous linear differential equations in which the coefficients are entire functions of finite [p, q]-order. We get the results about [p, q]-order and the [p, q]-convergence exponent of solutions for such equations.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"33 - 53"},"PeriodicalIF":0.9,"publicationDate":"2018-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2017.1413065","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44085186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-01-02DOI: 10.1080/1726037X.2017.1413064
A. Mesón, F. Vericat
ABSTRACT In a recent article, Chung and Takahashi (Erg. Th & Dynan. Sys. 34, 1116 (2014)) effected a multifractal description of the Birkhoff spectrum for a set of quadratic one dimensional functions known as the Benedicks-Carleson maps. They obtained a variational formula for the dimension spectrum of Birkhoff averages. In this article we try to complete the analysis studying the spectrum of quotients of Birkhoff averages.
{"title":"Multifractal spectrum of quotients of Birkhoff averages for a family of quadratic maps","authors":"A. Mesón, F. Vericat","doi":"10.1080/1726037X.2017.1413064","DOIUrl":"https://doi.org/10.1080/1726037X.2017.1413064","url":null,"abstract":"ABSTRACT In a recent article, Chung and Takahashi (Erg. Th & Dynan. Sys. 34, 1116 (2014)) effected a multifractal description of the Birkhoff spectrum for a set of quadratic one dimensional functions known as the Benedicks-Carleson maps. They obtained a variational formula for the dimension spectrum of Birkhoff averages. In this article we try to complete the analysis studying the spectrum of quotients of Birkhoff averages.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"16 1","pages":"17 - 32"},"PeriodicalIF":0.9,"publicationDate":"2018-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2017.1413064","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48886200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-08-16DOI: 10.1080/1726037X.2020.1774156
Z. N. Ahmadabadi, F. A. Z. Shirazi
Abstract Suppose X is a finite discrete space with at least two elements, Γ is a nonempty countable set, and consider self–map φ: Γ → Γ. We prove that the generalized shift σφ : X Γ →X Γ with σφ((Xα) α ∈Γ) = (Xφ (α))α∈Γ (for (Xα ) α ∈Γ ∈ X Γ) is: distributional chaotic (uniform, type 1, type 2) if and only if φ : Γ → Γ has at least a non-quasi-periodic point, dense distributional chaotic if and only if φ : Γ → Γ does not have any periodic point, transitive distributional chaotic if and only if φ : Γ → Γ is one–to–one without any periodic point. We complete the text by counterexamples.
{"title":"Distributional Chaotic Generalized Shifts","authors":"Z. N. Ahmadabadi, F. A. Z. Shirazi","doi":"10.1080/1726037X.2020.1774156","DOIUrl":"https://doi.org/10.1080/1726037X.2020.1774156","url":null,"abstract":"Abstract Suppose X is a finite discrete space with at least two elements, Γ is a nonempty countable set, and consider self–map φ: Γ → Γ. We prove that the generalized shift σφ : X Γ →X Γ with σφ((Xα) α ∈Γ) = (Xφ (α))α∈Γ (for (Xα ) α ∈Γ ∈ X Γ) is: distributional chaotic (uniform, type 1, type 2) if and only if φ : Γ → Γ has at least a non-quasi-periodic point, dense distributional chaotic if and only if φ : Γ → Γ does not have any periodic point, transitive distributional chaotic if and only if φ : Γ → Γ is one–to–one without any periodic point. We complete the text by counterexamples.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"18 1","pages":"53 - 70"},"PeriodicalIF":0.9,"publicationDate":"2017-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2020.1774156","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45332230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-03DOI: 10.1080/1726037X.2017.1390191
V. Govindaraj, R. K. George
Abstract In this paper, a set of equivalent conditions for observability and controllability of linear fractional dynamical systems represented by the fractional differential equation in the sense of Caputo fractional derivative of order α ϵ (0,1] are established by using the tools of linear bounded operators. Examples are included to illustrate the theoretical results.
{"title":"Functional approach to observability and controllability of linear fractional dynamical systems","authors":"V. Govindaraj, R. K. George","doi":"10.1080/1726037X.2017.1390191","DOIUrl":"https://doi.org/10.1080/1726037X.2017.1390191","url":null,"abstract":"Abstract In this paper, a set of equivalent conditions for observability and controllability of linear fractional dynamical systems represented by the fractional differential equation in the sense of Caputo fractional derivative of order α ϵ (0,1] are established by using the tools of linear bounded operators. Examples are included to illustrate the theoretical results.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"15 1","pages":"111 - 129"},"PeriodicalIF":0.9,"publicationDate":"2017-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2017.1390191","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45939760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-03DOI: 10.1080/1726037X.2017.1411043
J. Singh, T. O. Amuda
Abstract The research paper under consideration investigates the motion in the vicinity of triangular equilibrium points of the circular restricted three-body problem of a passively gravitating dust particle in the gravitational field for the binaries system (Kruger 60 and Achird). The two bodies of the binary are both oblate radiating stars possessing P-R drag. The position of triangular equilibrium points of the particle is seen to be affected by oblateness, radiation and P-R drag. In our numerical exploration of the binary system Kruger 60 and Achird, we computed the radiation factors qi (i= 1,2) and the velocity of light cd which is a component of the P-R drag. The points are unstable due to the presence of a positive real part of the complex roots.
{"title":"Effects of Poynting-Robertson (P-R) drag, radiation, and oblateness on motion around the L4,5 equilibrium points in the CR3BP","authors":"J. Singh, T. O. Amuda","doi":"10.1080/1726037X.2017.1411043","DOIUrl":"https://doi.org/10.1080/1726037X.2017.1411043","url":null,"abstract":"Abstract The research paper under consideration investigates the motion in the vicinity of triangular equilibrium points of the circular restricted three-body problem of a passively gravitating dust particle in the gravitational field for the binaries system (Kruger 60 and Achird). The two bodies of the binary are both oblate radiating stars possessing P-R drag. The position of triangular equilibrium points of the particle is seen to be affected by oblateness, radiation and P-R drag. In our numerical exploration of the binary system Kruger 60 and Achird, we computed the radiation factors qi (i= 1,2) and the velocity of light cd which is a component of the P-R drag. The points are unstable due to the presence of a positive real part of the complex roots.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"15 1","pages":"177 - 200"},"PeriodicalIF":0.9,"publicationDate":"2017-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2017.1411043","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47436271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-03DOI: 10.1080/1726037X.2017.1390192
U. V. Chetana, B. Shankar
Abstract We try to find chaotic dynamical systems by extending some simple continuous functions defined on ℚp, to functions defined on Aℤ, where A = {0,1,2, , p — 1}. A combination of the powers of the shift map with addition of a constant in ℚp, gives rise to chaotic dynamical systems, conjugate to powers of the shift map. By extending the addition in ℤp, to the whole of Aℤ, and combining with powers of the shift map, we get an expansive map with the same topological entropy as that of powers of the shift. We also obtain two more positively expansive maps with positive entropy.
摘要:我们尝试将定义在π (n)上的简单连续函数推广到定义在A (n)上的函数，其中A = {0,1,2，， p - 1}。移位映射的幂加上一个常数的组合，得到了与移位映射的幂共轭的混沌动力系统。通过将这个加法扩展到整个A，并结合移位映射的幂，我们得到了一个与移位映射的幂具有相同拓扑熵的扩展映射。我们还得到了两个具有正熵的正扩张映射。
{"title":"Chaotic dynamical systems on symbolic spaces","authors":"U. V. Chetana, B. Shankar","doi":"10.1080/1726037X.2017.1390192","DOIUrl":"https://doi.org/10.1080/1726037X.2017.1390192","url":null,"abstract":"Abstract We try to find chaotic dynamical systems by extending some simple continuous functions defined on ℚp, to functions defined on Aℤ, where A = {0,1,2, , p — 1}. A combination of the powers of the shift map with addition of a constant in ℚp, gives rise to chaotic dynamical systems, conjugate to powers of the shift map. By extending the addition in ℤp, to the whole of Aℤ, and combining with powers of the shift map, we get an expansive map with the same topological entropy as that of powers of the shift. We also obtain two more positively expansive maps with positive entropy.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"15 1","pages":"131 - 146"},"PeriodicalIF":0.9,"publicationDate":"2017-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2017.1390192","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44102341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-07-03DOI: 10.1080/1726037X.2017.1390847
T. Bayrakdar, A. A. Ergin
Abstract Hamiltonian vector field, Poisson vector field and the gradient of Hamiltonian function defines Darboux frame along an integral curve of a Hamiltonian dynamical system on a surface whose normal vector field corresponds to the Poisson structure for a given Hamiltonian system. We show that the existence of compatible Poisson structures determined by the normal legs of the Darboux frame is resolved to the characteristic equation for the Weingarten map. We also show that a Hamiltonian dynamical system in three dimensions has bi-Hamiltonian representation determined by the normal legs of Frenet-Serret triad if and only if an integral curve of Hamiltonian vector field is both a geodesic and a line of curvature.
{"title":"Hamiltonian dynamical systems and geometry of surfaces in 3-D","authors":"T. Bayrakdar, A. A. Ergin","doi":"10.1080/1726037X.2017.1390847","DOIUrl":"https://doi.org/10.1080/1726037X.2017.1390847","url":null,"abstract":"Abstract Hamiltonian vector field, Poisson vector field and the gradient of Hamiltonian function defines Darboux frame along an integral curve of a Hamiltonian dynamical system on a surface whose normal vector field corresponds to the Poisson structure for a given Hamiltonian system. We show that the existence of compatible Poisson structures determined by the normal legs of the Darboux frame is resolved to the characteristic equation for the Weingarten map. We also show that a Hamiltonian dynamical system in three dimensions has bi-Hamiltonian representation determined by the normal legs of Frenet-Serret triad if and only if an integral curve of Hamiltonian vector field is both a geodesic and a line of curvature.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"15 1","pages":"163 - 176"},"PeriodicalIF":0.9,"publicationDate":"2017-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2017.1390847","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45094456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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