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Journal of Dynamics and Differential Equations最新文献

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Entropy for Three-dimensional Vector Fields 三维矢量场的熵
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-03 DOI: 10.1007/s10884-024-10383-6
Fei Li, Wanlou Wu
{"title":"Entropy for Three-dimensional Vector Fields","authors":"Fei Li, Wanlou Wu","doi":"10.1007/s10884-024-10383-6","DOIUrl":"https://doi.org/10.1007/s10884-024-10383-6","url":null,"abstract":"<p>In this paper, we show that for any <span>(C^1)</span> three-dimensional vector fields with positive topological entropy, the topological entropy can be approximated by horseshoes. Precisely, for any <span>(C^1)</span> three-dimensional vector field <i>X</i> with positive topological entropy, there exists a vector field <i>Y</i> arbitrarily close (in the <span>(C^1)</span> topology) to <i>X</i> exhibiting a horseshoe <span>(Lambda )</span> such that the topological entropy of <i>Y</i> restricted on <span>(Lambda )</span> can arbitrarily approximate the topological entropy of <i>X</i>. This extends a classical result (Katok in Inst Hautes Études Sci Publ Math 51:137–173, 1980) of Katok for <span>(C^{1+alpha }(alpha &gt;0))</span> surface diffeomorphisms and a result (Wu and Liu in Proc Am Math Soc 148(1):223–233, 2020) for <span>(C^1)</span> surface diffeomorphisms.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"217 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141884929","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
Entropy Spectrum of Lyapunov Exponents for Typical Cocycles 典型循环的李亚普诺夫指数熵谱
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-20 DOI: 10.1007/s10884-024-10379-2
Reza Mohammadpour
{"title":"Entropy Spectrum of Lyapunov Exponents for Typical Cocycles","authors":"Reza Mohammadpour","doi":"10.1007/s10884-024-10379-2","DOIUrl":"https://doi.org/10.1007/s10884-024-10379-2","url":null,"abstract":"<p>In this paper, we study the size of the level sets of all Lyapunov exponents. For typical cocycles, we establish a variational relation between the topological entropy of the level sets of Lyapunov exponents and the topological pressure of the generalized singular value function.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"64 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744188","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
Periodic Solutions for a Class of Nonlinear Differential Equations 一类非线性微分方程的周期性解法
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-02 DOI: 10.1007/s10884-024-10375-6
Huafeng Xiao, Juan Xiao, Jianshe Yu
{"title":"Periodic Solutions for a Class of Nonlinear Differential Equations","authors":"Huafeng Xiao, Juan Xiao, Jianshe Yu","doi":"10.1007/s10884-024-10375-6","DOIUrl":"https://doi.org/10.1007/s10884-024-10375-6","url":null,"abstract":"<p>In this paper, we address the existence and multiplicity of 2-periodic solutions to differential equations with a distributed delay of the form </p><span>$$begin{aligned} x^{prime }(t)=fBig [int _{t-1}^t gbig (x(s)big ) d sBig ],quad x in textbf{R}^N. end{aligned}$$</span><p>Combining Kaplan–Yorke’s method with pseudoindex theory, we estimate the number of periodic solutions when the equations are both resonant and nonresonant. More specifically, we define two indices using asymptotic linear coefficient matrices at the origin and at infinity. Then the lower bound on the number of periodic solutions to the equations is estimated by the indices. Finally, two examples are given to illustrate our results.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"44 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503065","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
Highly Non-contractive Iterated Function Systems on Euclidean Space Can Have an Attractor 欧几里得空间上的高度非契约迭代函数系统可以有一个吸引器
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-06-14 DOI: 10.1007/s10884-024-10367-6
Krzysztof Leśniak, Nina Snigireva, Filip Strobin, Andrew Vince
{"title":"Highly Non-contractive Iterated Function Systems on Euclidean Space Can Have an Attractor","authors":"Krzysztof Leśniak, Nina Snigireva, Filip Strobin, Andrew Vince","doi":"10.1007/s10884-024-10367-6","DOIUrl":"https://doi.org/10.1007/s10884-024-10367-6","url":null,"abstract":"<p>Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. Moreover, contractivity of the functions in the IFS has been central to the theory of iterated functions systems. If the functions in the IFS are contractions, then the IFS is guaranteed to have a unique attractor. The converse question, does the existence of an attractor imply that the IFS is contractive, originates in a 1959 work by Bessaga which proves a converse to the contraction mapping theorem. Although a converse is true in that case, it is known that it does not always hold for an IFS. In general, there do exist IFSs with attractors and which are not contractive. However, in the context of IFSs in Euclidean space, this question has been open. In this paper we show that a highly non-contractive iterated function system in Euclidean space can have an attractor. In order to do that, we introduce the concept of an <i>L</i>-expansive map, i.e., a map that has Lipschitz constant strictly greater than one under any remetrization. This is necessitated by the absence of positively expansive maps on the interval.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"23 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503066","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
On the Well-Posedness of Two Driven-Damped Gross–Pitaevskii-Type Models for Exciton-Polariton Condensates 关于激子-极坐标凝聚态的两种驱动-阻尼格罗斯-皮塔耶夫斯基模型的拟合优度
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-05-15 DOI: 10.1007/s10884-024-10359-6
Jakob Möller, Jesus Sierra
{"title":"On the Well-Posedness of Two Driven-Damped Gross–Pitaevskii-Type Models for Exciton-Polariton Condensates","authors":"Jakob Möller, Jesus Sierra","doi":"10.1007/s10884-024-10359-6","DOIUrl":"https://doi.org/10.1007/s10884-024-10359-6","url":null,"abstract":"<p>We study the well-posedness of two systems modeling the non-equilibrium dynamics of pumped decaying Bose–Einstein condensates. In particular, we present the local theory for rough initial data using the Fourier restricted norm method introduced by Bourgain. We extend the result globally for initial data in <span>(L^{2})</span>.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"47 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060400","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
First-time Sensitive Homeomorphisms 首次敏感同构
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-04-09 DOI: 10.1007/s10884-024-10362-x
Mayara Antunes, Bernardo Carvalho
{"title":"First-time Sensitive Homeomorphisms","authors":"Mayara Antunes, Bernardo Carvalho","doi":"10.1007/s10884-024-10362-x","DOIUrl":"https://doi.org/10.1007/s10884-024-10362-x","url":null,"abstract":"<p>We introduce first-time sensitivity for a homeomorphism of a compact metric space, that is a condition on the first increasing times of open balls of the space. Continuum-wise expansive homeomorphisms, the shift map on the Hilbert cube, and also some partially hyperbolic diffeomorphisms satisfy this condition. We prove the existence of local unstable continua satisfying similar properties with the local unstable continua of continuum-wise expansive homeomorphisms, but assuming first-time sensitivity. As a consequence we prove that first-time sensitivity (with some additional technical assumptions) implies positive topological entropy.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"85 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601659","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
Non-collision Orbits for a Class of Singular Hamiltonian Systems on the Plane with Weak Force Potentials 平面上一类具有弱作用力势能的奇异哈密顿系统的非碰撞轨道
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-04-04 DOI: 10.1007/s10884-024-10363-w
Mohamed Antabli, Morched Boughariou
{"title":"Non-collision Orbits for a Class of Singular Hamiltonian Systems on the Plane with Weak Force Potentials","authors":"Mohamed Antabli, Morched Boughariou","doi":"10.1007/s10884-024-10363-w","DOIUrl":"https://doi.org/10.1007/s10884-024-10363-w","url":null,"abstract":"<p>We study the existence of non-collision orbits for a class of singular Hamiltonian systems </p><span>$$begin{aligned} ddot{q}+ V'(q)=0 end{aligned}$$</span><p>where <span>(q:{mathbb {R}} longrightarrow {mathbb {R}}^2)</span> and <span>(Vin C^2({mathbb {R}}^2 {setminus } {e},, {mathbb {R}}))</span> is a potential with a singularity at a point <span>(enot =0)</span>. We consider <i>V</i> which behaves like <span>(displaystyle -1/|q-e|^alpha )</span> as <span>( qrightarrow e )</span> with <span>(alpha in ]0,2[.)</span> Under the assumption that 0 is a strict global maximum for <i>V</i>, we establish the existence of a homoclinic orbit emanating from 0. Moreover, in case <span>(displaystyle V(q) longrightarrow 0)</span> as <span>(|q|rightarrow +infty )</span>, we prove the existence of a heteroclinic orbit “at infinity\" i.e. a solution <i>q</i> such that </p><span>$$begin{aligned} lim _{trightarrow -infty } q(t)=0,,, lim _{t rightarrow +infty }|q(t)|=+infty ,, hbox {and} , lim _{t rightarrow pm infty }dot{q}(t)=0. end{aligned}$$</span>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"35 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602200","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
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