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Journal of Dynamics and Differential Equations最新文献

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Chaos of Induced Set-Valued Dynamical Systems on Uniform Spaces 统一空间上诱导集值动态系统的混沌问题
IF 1.3 4区 数学 Q1 Mathematics
Journal of Dynamics and Differential Equations
Pub Date : 2024-06-11 DOI: 10.1007/s10884-024-10374-7
Hua Shao
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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 Q1 MATHEMATICS
Journal of Dynamics and Differential Equations
Pub Date : 2024-06-08 DOI: 10.1007/s10884-024-10373-8
Yurii Averboukh

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.

我们研究了一个非局部平衡方程，它描述了一个由无限多个相同粒子组成的系统的演化过程，这些粒子沿着确定性动力学运动，也可以消失或产生弹簧。在这种情况下，平衡方程的解是在非负度量空间中考虑的。我们证明了所研究的非局部平衡方程的叠加原理。此外，我们将源/汇项解释为从/到远处点的跃迁概率率。利用这一思想，并用非线性马尔可夫链取代每个粒子的确定性动力学，我们用一个 ODE 系统的解来近似平衡方程的解，并评估相应的近似率。这一结果可用于构建非局部平衡方程的数值解。
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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 Q1 Mathematics
Journal of Dynamics and Differential Equations
Pub Date : 2024-06-04 DOI: 10.1007/s10884-024-10370-x
Hiroki Takahasi

We investigate mixing properties of piecewise affine non-Markovian maps acting on ([0,1]^2) or ([0,1]^3) and preserving the Lebesgue measure, which are natural generalizations of the heterochaos baker maps 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.

我们研究了作用于（[0,1]^2）或（[0,1]^3）并保留勒贝格度量的片断仿射非马尔可夫映射的混合特性，这些映射是Saiki等人（《非线性》34:5744-5761, 2021年）中介绍的heterochaos贝克映射的自然概括。这些映射是均匀膨胀或双曲基上的偏积，纤维方向是收缩和膨胀行为共存的中心。我们证明这些映射是所有阶的混合。对于以膨胀或收缩为中心的映射，我们建立了霍尔德函数的指数混合。利用这一结果，对于起源于形式语言理论的戴克系统，我们就其两个共存的最大熵的遍历度量建立了霍尔德函数的指数混合。
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引用次数: 0
Uniform Stability for a Semilinear Laminated Timoshenko Beams Posed in Inhomogeneous Medium with Localized Nonlinear Damping 在具有局部非线性阻尼的非均质介质中求解的半线性层叠季莫申科梁的均匀稳定性
IF 1.3 4区 数学 Q1 Mathematics
Journal of Dynamics and Differential Equations
Pub Date : 2024-05-21 DOI: 10.1007/s10884-024-10369-4
Sabeur Mansouri
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引用次数: 0
Synchronous and Asynchronous Solutions for Some Nonlocal Dispersal Equations 一些非局部分散方程的同步和异步解法
IF 1.3 4区 数学 Q1 Mathematics
Journal of Dynamics and Differential Equations
Pub Date : 2024-05-17 DOI: 10.1007/s10884-024-10368-5
Jian-Wen Sun, Wen Tao
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引用次数: 0
Orbifold Hamiltonian Structures of Certain Quasi-Painlevé Equations 某些准潘列夫方程的轨道哈密顿结构
IF 1.3 4区 数学 Q1 Mathematics
Journal of Dynamics and Differential Equations
Pub Date : 2024-05-15 DOI: 10.1007/s10884-024-10352-z
G. Filipuk, A. Stokes
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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 Q1 Mathematics
Journal of Dynamics and Differential Equations
Pub Date : 2024-05-15 DOI: 10.1007/s10884-024-10359-6
Jakob Möller, Jesus Sierra

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 (L^{2}).

我们研究了两个模拟抽运衰变玻色-爱因斯坦凝聚体非平衡态动力学的系统的好拟性。特别是，我们使用布尔甘（Bourgain）引入的傅立叶限制规范法，提出了粗糙初始数据的局部理论。我们将这一结果扩展到了(L^{2})中初始数据的全局。
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引用次数: 0
Blow Up for Klein–Gordon Equation with Nonlocal Operator and Trudinger–Moser Nonlinearity 具有非局部算子和特鲁丁格-莫泽非线性的克莱因-戈登方程的膨胀问题
IF 1.3 4区 数学 Q1 Mathematics
Journal of Dynamics and Differential Equations
Pub Date : 2024-04-23 DOI: 10.1007/s10884-024-10366-7
P. C. Carrião, O. Miyagaki, André Vicente
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引用次数: 0
Long Time Dynamics of Quasi-linear Hamiltonian Klein–Gordon Equations on the Circle 圆周上准线性哈密顿克莱因-戈登方程的长时动力学
IF 1.3 4区 数学 Q1 Mathematics
Journal of Dynamics and Differential Equations
Pub Date : 2024-04-22 DOI: 10.1007/s10884-024-10365-8
R. Feola, Filippo Giuliani
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引用次数: 0
First-time Sensitive Homeomorphisms 首次敏感同构
IF 1.3 4区 数学 Q1 Mathematics
Journal of Dynamics and Differential Equations
Pub Date : 2024-04-09 DOI: 10.1007/s10884-024-10362-x
Mayara Antunes, Bernardo Carvalho

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.

我们介绍了紧凑度量空间同构的首次敏感性，即空间开球的首次增大次数的条件。连续膨胀同构、希尔伯特立方体上的移动映射以及一些部分双曲差同构都满足这个条件。我们证明了局部不稳定连续面的存在，其性质与连续膨胀同态的局部不稳定连续面相似，但假定了首次敏感性。因此，我们证明了首次敏感性（加上一些额外的技术假设）意味着正拓扑熵。
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引用次数: 0
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