Attractors of dynamical systems in locally compact spaces

Gang Li ,Yuxia Gao

doi:10.1515/math-2019-0037

Abstract

Abstract In this article the properties of attractors of dynamical systems in locally compact metric space are discussed. Existing conditions of attractors and related results are obtained by the near isolating block which we present.

Highlights

The dynamical system theory studies the rules of changes in the state which depends on time
In [5], the limit set of a neighborhood was used in the de nition of an attractor, and in
Assume that the set N is a bounded near isolating block of Rn, i.e., for each x ∈ ∂N, x · R− ∩ ExtN ≠, so we only prove if α(x, π) ≠ for x ∈ ∂N, α(x, π) ∩ ExtN ≠

Summary

Introduction

The dynamical system theory studies the rules of changes in the state which depends on time. To give the existing conditions of attractors of dynamical systems, we need rst give the properties of the limit set, which have been proven in [ ], [ ] and will be used in our main theorems.

Results

Conclusion