Topological stability and shadowing of zero-dimensional dynamical systems

Noriaki Kawaguchi

doi:10.3934/dcds.2019115

Article Contents

2019, Volume 39, Issue 5: 2743-2761. Doi: 10.3934/dcds.2019115

This issue Previous Article Explicit estimates on positive supersolutions of nonlinear elliptic equations and applications Next Article Local wellposedness for the critical nonlinear Schrödinger equation on

$ \mathbb{T}^3 $

Topological stability and shadowing of zero-dimensional dynamical systems

Noriaki Kawaguchi

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro, Tokyo 153-8914, Japan

Received: May 2018

Revised: September 2018

Published: January 2019

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Abstract

In this paper, we examine the notion of topological stability and its relation to the shadowing properties in zero-dimensional spaces. Several counter-examples on the topological stability and the shadowing properties are given. Also, we prove that any topologically stable (in a modified sense) homeomorphism of a Cantor space exhibits only simple typical dynamics.

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Mathematics Subject Classification: 54H20, 37C50.

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References

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