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Journal of Dynamics and Differential Equations最新文献

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Periodic Generalized Birkhoff Solutions and Farey Intervals for Monotone Recurrence Relations 单调递推关系的周期性广义伯克霍夫解和法雷区间
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-04-04 DOI: 10.1007/s10884-024-10364-9
{"title":"Periodic Generalized Birkhoff Solutions and Farey Intervals for Monotone Recurrence Relations","authors":"","doi":"10.1007/s10884-024-10364-9","DOIUrl":"https://doi.org/10.1007/s10884-024-10364-9","url":null,"abstract":"<h3>Abstract</h3> <p>The aim of this paper is to extend the results associated with periodic orbits from two-dimensions to higher-dimensions. Because of the one-to-one correspondence between solutions for the monotone recurrence relation and orbits for the induced high-dimensional cylinder twist map, we consider the system of solutions for monotone recurrence relations instead. By introducing intersections of type (<em>k</em>, <em>l</em>), we propose the definition of generalized Birkhoff solutions, generalizing the concept of Birkhoff solutions. We show that if there is a (<em>p</em>, <em>q</em>)-periodic solution which is not a generalized Birkhoff solution, then the system has positive topological entropy and the Farey interval of <em>p</em>/<em>q</em> is contained in the rotation set.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"300 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601653","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}
引用次数: 0
Boundedness of Solutions of Nonautonomous Degenerate Logistic Equations 非自治退化逻辑方程解的有界性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-03-25 DOI: 10.1007/s10884-024-10354-x
José M. Arrieta, Marcos Molina-Rodríguez, Lucas A. Santos
{"title":"Boundedness of Solutions of Nonautonomous Degenerate Logistic Equations","authors":"José M. Arrieta, Marcos Molina-Rodríguez, Lucas A. Santos","doi":"10.1007/s10884-024-10354-x","DOIUrl":"https://doi.org/10.1007/s10884-024-10354-x","url":null,"abstract":"<p>In this work we analyze the boundedness properties of the solutions of a nonautonomous parabolic degenerate logistic equation in a bounded domain. The equation is degenerate in the sense that the logistic nonlinearity vanishes in a moving region, <i>K</i>(<i>t</i>), inside the domain. The boundedness character of the solutions depends not only on, roughly speaking, the first eigenvalue of the Laplace operator in <i>K</i>(<i>t</i>) but also on the way this moving set evolves inside the domain and in particular on the speed at which it moves.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"87 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302716","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}
引用次数: 0
$$C^{infty }$$ -Regularization by Noise of Singular ODE’s $$C^{infty}$$-奇异 ODE 的噪声规则化
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-03-25 DOI: 10.1007/s10884-024-10355-w
Oussama Amine, David Baños, Frank Proske
{"title":"$$C^{infty }$$ -Regularization by Noise of Singular ODE’s","authors":"Oussama Amine, David Baños, Frank Proske","doi":"10.1007/s10884-024-10355-w","DOIUrl":"https://doi.org/10.1007/s10884-024-10355-w","url":null,"abstract":"<p>In this paper we construct a new type of noise of fractional nature that has a strong regularizing effect on differential equations. We consider an equation driven by a highly irregular vector field and study the effect of this noise on such dynamical systems. We employ a new method to prove existence and uniqueness of global strong solutions, where classical methods fail because of the “roughness” and non-Markovianity of the driving process. In addition, we prove the rather remarkable property that such solutions are infinitely many times classically differentiable with respect to the initial condition in spite of the vector field being discontinuous. The technique used in this article corresponds, in a certain sense, to the Nash–Moser iterative scheme in combination with a new concept of “higher order averaging operators along highly fractal stochastic curves”. This approach may provide a general principle for the study of regularization by noise effects in connection with important classes of partial differential equations.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"30 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302671","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}
引用次数: 0
Building Expansion for Generalizations of Viana Maps 维亚纳地图泛化的构建扩展
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-03-25 DOI: 10.1007/s10884-024-10357-8
Vanderlei Horita, Nivaldo Muniz, Olivier Sester
{"title":"Building Expansion for Generalizations of Viana Maps","authors":"Vanderlei Horita, Nivaldo Muniz, Olivier Sester","doi":"10.1007/s10884-024-10357-8","DOIUrl":"https://doi.org/10.1007/s10884-024-10357-8","url":null,"abstract":"<p>We study a family of skew-products of smooth functions having a unique critical point of degree <span>(Dge 2)</span> over a strongly expanding map of the circle and prove that these systems admit two positive Lyapunov exponents. This extends an analogous result of Viana who considered, in the seminal paper (Viana in Inst Hautes Études Sci Publ Math 85:63–96, 1997), the quadratic case <span>(D=2)</span>.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"86 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302667","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}
引用次数: 0
Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems 非连续系统中接近非光滑同线性周期的极限周期分岔
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-03-25 DOI: 10.1007/s10884-024-10358-7
Duo Hua, Xingbo Liu
{"title":"Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems","authors":"Duo Hua, Xingbo Liu","doi":"10.1007/s10884-024-10358-7","DOIUrl":"https://doi.org/10.1007/s10884-024-10358-7","url":null,"abstract":"<p>The main aim of this paper is to study the limit cycle bifurcations near the homoclinic cycle in the discontinuous systems. Based on the impoved Lin’s method, we establish the bifurcation equation, which presents the existence of limit cycles bifurcated from nonsmooth homoclinic cycles under perturbation. Furthermore, we give an example to support our conclusions. After solving a boundary value problem with numerical tools, we provide the exact parameter values for the system having a limit cycle.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"12 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302767","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}
引用次数: 0
Global Attractors for a Class of Discrete Dynamical Systems 一类离散动力系统的全局吸引子
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-03-25 DOI: 10.1007/s10884-024-10356-9
{"title":"Global Attractors for a Class of Discrete Dynamical Systems","authors":"","doi":"10.1007/s10884-024-10356-9","DOIUrl":"https://doi.org/10.1007/s10884-024-10356-9","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we study the existence of global attractors for a class of discrete dynamical systems naturally originated from impulsive dynamical systems. We establish sufficient conditions for the existence of a discrete global attractor. Moreover, we investigate the relationship among different types of global attractors, i.e., the attractor <span> <span>({mathcal {A}})</span> </span> of a continuous dynamical system, the attractor <span> <span>(tilde{{mathcal {A}}})</span> </span> of an impulsive dynamical system and the attractor <span> <span>(hat{{mathcal {A}}})</span> </span> of a discrete dynamical system. Two applications are presented, one involving an integrate-and-fire neuron model, and the other involving a nonlinear reaction-diffusion initial boundary value problem.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"30 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302759","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}
引用次数: 0
Birkhoff Program for Geodesic Flows of Surfaces and Applications: Homoclinics 表面大地流的伯克霍夫程序及其应用：同次元
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-03-09 DOI: 10.1007/s10884-024-10349-8
Gonzalo Contreras, Fernando Oliveira
{"title":"Birkhoff Program for Geodesic Flows of Surfaces and Applications: Homoclinics","authors":"Gonzalo Contreras, Fernando Oliveira","doi":"10.1007/s10884-024-10349-8","DOIUrl":"https://doi.org/10.1007/s10884-024-10349-8","url":null,"abstract":"<p>We show that a Kupka–Smale riemannian metric on a closed surface contains a finite primary set of closed geodesics, i.e. they intersect any other geodesic and divide the surface into simply connected regions. From them we obtain a finite set of disjoint surfaces of section of genera 0 or 1, which intersect any orbit of the geodesic flow. As an application we obtain that the geodesic flow of a Kupka–Smale riemannian metric on a closed surface has homoclinic orbits for all branches of all of its hyperbolic closed geodesics.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"220 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075780","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}
引用次数: 0
Chain Recurrence and Selgrade’s Theorem for Affine Flows 仿射流的链式递推和塞尔格拉德定理
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-03-04 DOI: 10.1007/s10884-024-10351-0
Fritz Colonius, Alexandre J. Santana
{"title":"Chain Recurrence and Selgrade’s Theorem for Affine Flows","authors":"Fritz Colonius, Alexandre J. Santana","doi":"10.1007/s10884-024-10351-0","DOIUrl":"https://doi.org/10.1007/s10884-024-10351-0","url":null,"abstract":"<p>Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade’s theorem is determined. The results are illustrated by an application to affine control systems with bounded control range.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"71 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140032853","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}
引用次数: 0
Invariant Manifolds for a PDE-ODE Coupled System PDE-ODE 耦合系统的不变量频域
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-02-28 DOI: 10.1007/s10884-024-10353-y
Xingjie Yan, Kun Yin, Xin-Guang Yang, Alain Miranville
{"title":"Invariant Manifolds for a PDE-ODE Coupled System","authors":"Xingjie Yan, Kun Yin, Xin-Guang Yang, Alain Miranville","doi":"10.1007/s10884-024-10353-y","DOIUrl":"https://doi.org/10.1007/s10884-024-10353-y","url":null,"abstract":"<p>The aim of this paper is to construct invariant manifolds for a coupled system, consisting of a parabolic equation and a second-order ordinary differential equation, set on <span>(mathbb {T}^3)</span> and subject to periodic boundary conditions. Notably, the “spectral gap condition\" does not hold for the system under consideration, leading to the use of the spatial averaging principle, together with the graph transform method. This approach facilitates the construction of the relevant invariant manifold, characterized by attributes such as Lipschitz continuity, local invariance, infinite dimensionality, and exponential tracking, thus mirroring the properties traditionally associated with a classical global manifold.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"25 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140006453","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}
引用次数: 0
Rigidity and Absolute Continuity of Foliations of Anosov Endomorphisms 阿诺索夫内定形叶形的刚性与绝对连续性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-02-26 DOI: 10.1007/s10884-024-10350-1
Fernando Micena
{"title":"Rigidity and Absolute Continuity of Foliations of Anosov Endomorphisms","authors":"Fernando Micena","doi":"10.1007/s10884-024-10350-1","DOIUrl":"https://doi.org/10.1007/s10884-024-10350-1","url":null,"abstract":"<p>We found a dichotomy involving rigidity and measure of maximal entropy of a <span>(C^{infty })</span>-special Anosov endomorphism of the 2-torus. Considering <span>(widetilde{m} )</span> the measure of maximal entropy of a <span>(C^{infty })</span>-special Anosov endomorphism of the 2-torus, either <span>(widetilde{m})</span> satisfies the Pesin formula (in this case we get smooth conjugacy with the linearization) or there is a set <i>Z</i>, such that <span>(widetilde{m}(Z) = 1,)</span> but <i>Z</i> intersects every unstable leaf on a set of zero measure of the leaf. Also, we can characterize the absolute continuity of the intermediate foliation for a class of volume-preserving special Anosov endomorphisms of <span>(mathbb {T}^3)</span>.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"2016 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139981587","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}
引用次数: 0
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