<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Let f : M → M be a diffeomorphism on a closed smooth n(<italic>≥</italic> 2) dimensional manifold M. We show that C<sup>1</sup> generically, if a diffeomorphism f has the orbital shadowing property on locally maximal chain transitive sets which admits a dominated splitting then it is hyperbolic.</p></abstract>

Let f : M → M be a diffeomorphism on a closed smooth n(≥ 2) dimensional manifold M. We show that C1 generically, if a diffeomorphism f has the orbital shadowing property on locally maximal chain transitive sets which admits a dominated splitting then it is hyperbolic.

Orbital shadowing property on chain transitive sets for generic diffeomorphisms

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Orbital shadowing property on chain transitive sets for generic diffeomorphisms"}

Let f : M → M be a diffeomorphism on a closed smooth n(≥ 2) dimensional manifold M. We show that C1 generically, if a diffeomorphism f has the orbital...

Orbital shadowing property on chain transitive sets for generic diffeomorphisms

Published Online: Jul 16, 2020

Page range: 146 - 154

Received: Sep 18, 2018

DOI: https://doi.org/10.2478/ausm-2020-0009

Keywords
shadowing, orbital shadowing, chain transitive set, homoclinic class, chain recurrence class, hyperbolic, generic

© 2020 Manseob Lee, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Orbital shadowing property on chain transitive sets for generic diffeomorphisms

Published Online: Jul 16, 2020

Page range: 146 - 154

Received: Sep 18, 2018

DOI: https://doi.org/10.2478/ausm-2020-0009

Keywordsshadowing, orbital shadowing, chain transitive set, homoclinic class, chain recurrence class, hyperbolic, generic

© 2020 Manseob Lee, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
shadowing, orbital shadowing, chain transitive set, homoclinic class, chain recurrence class, hyperbolic, generic