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Start Over Descriptor "secondary 37d20" Database Directory of Open Access Journals
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1. Asymptotic orbital shadowing property for diffeomorphisms

Author

Lee Manseob

Subjects
shadowing, limit shadowing, orbital limit shadowing, asymptotic orbital shadowing, chain transitive, hyperbolic, generic, primary 37c50, 37c20, secondary 37d20, Mathematics, QA1-939
Abstract

Let M be a closed smooth Riemannian manifold and let f : M → M be a diffeomorphism. We show that if f has the C1 robustly asymptotic orbital shadowing property then it is an Anosov diffeomorphism. Moreover, for a C1 generic diffeomorphism f, if f has the asymptotic orbital shadowing property then it is a transitive Anosov diffeomorphism. In particular, we apply our results to volume-preserving diffeomorphisms.

Published
2019
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