Asymptotic orbital shadowing property for diffeomorphisms

Open Mathematics

Lee Manseob¹ 

[1] Department of Mathematics, Mokwon University, Daejeon, 302-729, Korea;

关键词: shadowing;    limit shadowing;    orbital limit shadowing;    asymptotic orbital shadowing;    chain transitive;    hyperbolic;    generic;    primary 37c50;    37c20;    secondary 37d20;   

DOI  :  10.1515/math-2019-0002

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown