Attractors of Local Semiflows on Topological Spaces
Dynamical Systems
2015-07-06 v3
Abstract
In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.
Keywords
Cite
@article{arxiv.1504.03762,
title = {Attractors of Local Semiflows on Topological Spaces},
author = {Desheng Li and Youbin Xiong and Jintao Wang},
journal= {arXiv preprint arXiv:1504.03762},
year = {2015}
}
Comments
22 pages