A Type of the Shadowing Properties for Generic View Points

A Type of the Shadowing Properties for Generic View Points

We show that if a C 1 generic diffeomorphism of a closed smooth two-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it is Anosov. Moreover, if a C 1 generic vector field of a closed smooth three-dimensional manifold has the average shadowing...

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Veröffentlicht in:Axioms 2018-03, Vol.7 (1), p.18
1. Verfasser: Lee, Manseob
Format: Artikel
Sprache:eng
Schlagworte:
Anosov
asymptotic average shadowing
Asymptotic properties
average shadowing
Axiom A
chain transitive
generic
singular Axiom A
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Zusammenfassung:We show that if a C 1 generic diffeomorphism of a closed smooth two-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it is Anosov. Moreover, if a C 1 generic vector field of a closed smooth three-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it satisfies singular Axiom A without cycles.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms7010018