J. Korean Math. Soc. 2017; 54(3): 773-791
Online first article April 10, 2017 Printed May 1, 2017
https://doi.org/10.4134/JKMS.j160214
Copyright © The Korean Mathematical Society.
Desheng Li, Jintao Wang, and Youbing Xiong
Tianjin University, Tianjin University, Tianjin University
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: topological space, local semiflow, attractor, existence, stability, Lyapunov function, Morse decomposition
MSC numbers: 37B25, 54H20
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