Shadowable Chain Recurrence Classes for Generic Diffeomorphisms

Shadowable Chain Recurrence Classes for Generic Diffeomorphisms

Let Diff (M) be the space of diffeomorphisms of a closedC ∞manifoldM(dimM≥ 2) endowed with theC 1topology. In this paper we show that forC 1genericf∈ Diff (M), any shadowable chain recurrence classCf is hyperbolic if it contains a hyperbolic periodic point. 2010Mathematics Subject Classification. Pr...

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Veröffentlicht in:Taiwanese journal of mathematics 2016-04, Vol.20 (2), p.399-409
Hauptverfasser: Lee, Keonhee, Lee, Manseob
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvalues
Histological shadowing
Periodic orbits
Tangents
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Zusammenfassung:Let Diff (M) be the space of diffeomorphisms of a closedC ∞manifoldM(dimM≥ 2) endowed with theC 1topology. In this paper we show that forC 1genericf∈ Diff (M), any shadowable chain recurrence classCf is hyperbolic if it contains a hyperbolic periodic point. 2010Mathematics Subject Classification. Primary: 37C50; Secondary: 37C20. Key words and phrases. Chain recurrence class, Homoclinic class, Shadowing, Hyperbolic, Generic.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.20.2016.5815