Diffeomorphisms with the M0-shadowing Property

Authors
Zhang, Xu Wu, Xin Xing
Citation
Zhang, Xu et Wu, Xin Xing, Diffeomorphisms with the M0-shadowing Property, Acta mathematica Sinica. English series (Print) , 35(11), 2019, pp. 1760-1770
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
35
Issue
11
Year of publication
2019
Pages
1760 - 1770
Database
ACNP
SICI code
Abstract
This paper studies the .0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the .0-shadowing property is described by the set of all Anosov diffeomorphisms. The C1-stably .0-shadowing property on a non-trivial transitive set implies the diffeomorphism has a dominated splitting.