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2021 Topological stability and shadowing of dynamical systems from measure theoretical viewpoint
Jiandong Yin, Meihua Dong
Topol. Methods Nonlinear Anal. 58(1): 307-321 (2021). DOI: 10.12775/TMNA.2020.071

Abstract

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.

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Jiandong Yin. Meihua Dong. "Topological stability and shadowing of dynamical systems from measure theoretical viewpoint." Topol. Methods Nonlinear Anal. 58 (1) 307 - 321, 2021. https://doi.org/10.12775/TMNA.2020.071

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Published: 2021
First available in Project Euclid: 21 September 2021

Digital Object Identifier: 10.12775/TMNA.2020.071

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.58 • No. 1 • 2021
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