• Li, Desheng (School of Mathematics Center of Applied Mathematics Tianjin University) ;
  • Wang, Jintao (Center for Mathematical Sciences Huazhong University of Science and Technology) ;
  • Xiong, Youbing (School of Mathematics Tianjin University)
  • Received : 2016.04.01
  • Published : 2017.05.01


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.


topological space;local semiflow;attractor;existence;stability;Lyapunov function;Morse decomposition


Supported by : NSF of China


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