Open AccessTopological stability and shadowing of dynamical systems from measure theoretical viewpoint
Author(s) -
Jiandong Yin,
Meihua Dong
Publication year - 2021
Publication title -
topological methods in nonlinear analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.623
H-Index - 23
ISSN - 1230-3429
DOI - 10.12775/tmna.2020.071
Subject(s) - mathematics , measure (data warehouse) , homeomorphism (graph theory) , invariant measure , expansive , invariant (physics) , dynamical systems theory , pure mathematics , borel measure , topology (electrical circuits) , topological conjugacy , property (philosophy) , mathematical analysis , discrete mathematics , probability measure , combinatorics , computer science , ergodic theory , philosophy , compressive strength , physics , epistemology , quantum mechanics , mathematical physics , materials science , database , composite material
In this paper it is proved that a topologically stable invariant measure has no sinks or sources in its support; an expansive homeomorphism is topologically stable if it exhibits a topologically stable nonatomic Borel support measure and a continuous map has the shadowing property if there exists an invariant measure with the shadowing property such that each almost periodic point is contained in the support of the invariant measure.