Birkhoff中心与竞争动力系统的统计行为

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-07-15 DOI:10.1016/j.jde.2025.113623

Xi Sheng , Yi Wang , Yufeng Zhang

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引用次数: 0

摘要

我们研究了竞争动力系统Birkhoff中心的位置和结构，并给出了轨道的递归性和统计行为的综合描述。建立了Birkhoff中心的任何连通分量的有序结构二分法，即它要么是无序的，要么是由强有序平衡点组成的。此外，存在一个由不变量（n−1）单元组成的标准定义的可数不相交族F，使得Birkhoff中心的每个无序连通分量都位于这些单元中的一个上。我们进一步证明了不变测度支持的任何连通分量要么由强有序平衡点组成，要么位于f的一个元素上。特别是，任何三维竞争流的拓扑熵为0。

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Birkhoff center and statistical behavior of competitive dynamical systems

We investigate the location and structure of the Birkhoff center for competitive dynamical systems, and give a comprehensive description of recurrence and statistical behavior of orbits. An order-structure dichotomy is established for any connected component of the Birkhoff center, that is, either it is unordered, or it consists of strongly ordered equilibria. Moreover, there is a canonically defined countable disjoint family

F

of invariant

(n - 1)

-cells such that each unordered connected component of the Birkhoff center lies on one of these cells. We further show that any connected component of the supports of invariant measures either consists of strongly ordered equilibria, or lies on one element of

F

. In particular, any 3-dimensional competitive flow has topological entropy 0.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics