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Journal of Dynamics and Differential Equations最新文献

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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
Semiflows Strongly Focusing Monotone with Respect to High-Rank Cones: I. Generic Dynamics 相对于高容锥强聚焦单调的半流：I. 一般动力学
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-06-12 DOI: 10.1007/s10884-024-10372-9
Lirui Feng
{"title":"Semiflows Strongly Focusing Monotone with Respect to High-Rank Cones: I. Generic Dynamics","authors":"Lirui Feng","doi":"10.1007/s10884-024-10372-9","DOIUrl":"https://doi.org/10.1007/s10884-024-10372-9","url":null,"abstract":"<p>We consider a smooth semiflow strongly focusing monotone with respect to a cone of rank <i>k</i> on a Banach space. We obtain its generic dynamics, that is, semiorbits with initial data from an open and dense subset of any open bounded set either are pseudo-ordered or convergent to an equilibrium. For the case <span>(k=1)</span>, it is the celebrated Hirsch’s Generic Convergence Theorem. For the case <span>(k=2)</span>, we obtain the generic Poincaré-Bendixson Theorem.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"46 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502919","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
Nonlocal Balance Equation: Representation and Approximation of Solution 非局部平衡方程：解的表示与近似
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-06-08 DOI: 10.1007/s10884-024-10373-8
Yurii Averboukh
{"title":"Nonlocal Balance Equation: Representation and Approximation of Solution","authors":"Yurii Averboukh","doi":"10.1007/s10884-024-10373-8","DOIUrl":"https://doi.org/10.1007/s10884-024-10373-8","url":null,"abstract":"<p>We study a nonlocal balance equation that describes the evolution of a system consisting of infinitely many identical particles those move along a deterministic dynamics and can also either disappear or give a spring. In this case, the solution of the balance equation is considered in the space of nonnegative measures. We prove the superposition principle for the examined nonlocal balance equation. Furthermore, we interpret the source/sink term as a probability rate of jumps from/to a remote point. Using this idea and replacing the deterministic dynamics of each particle by a nonlinear Markov chain, we approximate the solution of the balance equation by a solution of a system of ODEs and evaluate the corresponding approximation rate. This result can be used for construction of numerical solutions of the nonlocal balance equation.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551852","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
Exponential Mixing for Heterochaos Baker Maps and the Dyck System 异种贝克地图的指数混合和戴克系统
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-06-04 DOI: 10.1007/s10884-024-10370-x
Hiroki Takahasi
{"title":"Exponential Mixing for Heterochaos Baker Maps and the Dyck System","authors":"Hiroki Takahasi","doi":"10.1007/s10884-024-10370-x","DOIUrl":"https://doi.org/10.1007/s10884-024-10370-x","url":null,"abstract":"<p>We investigate mixing properties of piecewise affine non-Markovian maps acting on <span>([0,1]^2)</span> or <span>([0,1]^3)</span> and preserving the Lebesgue measure, which are natural generalizations of the <i>heterochaos baker maps</i> introduced in Saiki et al. (Nonlinearity 34:5744–5761, 2021). These maps are skew products over uniformly expanding or hyperbolic bases, and the fiber direction is a center in which both contracting and expanding behaviors coexist. We prove that these maps are mixing of all orders. For maps with a mostly expanding or contracting center, we establish exponential mixing for Hölder functions. Using this result, for the Dyck system originating in the theory of formal languages, we establish exponential mixing for Hölder functions with respect to its two coexisting ergodic measures of maximal entropy.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"41 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253028","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
A KAM Theorem for the Time Quasi-periodic Reversible Perturbations of Linear Wave Equations Beyond Brjuno Conditions 布儒诺条件之外线性波方程时间准周期可逆扰动的 KAM 定理
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-04-06 DOI: 10.1007/s10884-024-10360-z
{"title":"A KAM Theorem for the Time Quasi-periodic Reversible Perturbations of Linear Wave Equations Beyond Brjuno Conditions","authors":"","doi":"10.1007/s10884-024-10360-z","DOIUrl":"https://doi.org/10.1007/s10884-024-10360-z","url":null,"abstract":"<h3>Abstract</h3> <p>This paper is concerned with the existence of quasi-periodic response solutions (i.e., solutions that are quasi-periodic with the same frequencies as forcing term) for a class of forced reversible wave equations with derivative nonlinearity. The forcing frequency <span> <span>(omega in mathbb {R}^2)</span> </span> would be Liouvillean which is weaker than the usual Diophantine and Brjuno conditions. The derivative nonlinearity in the equation also leads to some difficulty in measure estimate. To overcome it, we also use the Töplitz–Lipschitz property of vector field. The proof is based on an infinite dimensional Kolmogorov–Arnold–Moser theorem for reversible systems.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"22 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601704","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 Structure of Entropy Solutions to the Riemann Problem for a Degenerate Nonlinear Parabolic Equation 论畸变非线性抛物方程黎曼问题的熵解结构
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-04-06 DOI: 10.1007/s10884-024-10361-y
{"title":"On the Structure of Entropy Solutions to the Riemann Problem for a Degenerate Nonlinear Parabolic Equation","authors":"","doi":"10.1007/s10884-024-10361-y","DOIUrl":"https://doi.org/10.1007/s10884-024-10361-y","url":null,"abstract":"<h3>Abstract</h3> <p>We find an explicit form of entropy solution to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and diffusion coefficients. It is demonstrated that this solution corresponds to the minimum point of some strictly convex function of a finite number of variables. We also discuss the limit when piecewise constant coefficients approximate the arbitrary ones.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"67 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602199","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
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