Year: 2023
Type: preprint
Abstract: 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 $\mathcal{F}$ 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 $\mathcal{F}$. In particular, any $3$-dimensional competitive flow has topological entropy $0$.
Source: arXiv (Cornell University)
Authors: Sheng, Xi, Wang, Yi, Zhang, Yufeng
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1908044709, G2333573991, G7485235633
OpenAlex ID: W4388685240