Partial hyperbolicity and homoclinic tangencies

Partial hyperbolicity and homoclinic tangencies

We show that any diffeomorphism of a compact manifold can be $C^1$ approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.

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Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2015-01, Vol.17 (1), p.1-49
Hauptverfasser: Crovisier, Sylvain, Sambarino, Martin, Yang, Dawei
Format: Artikel
Sprache:eng
Schlagworte:
Dynamical systems and ergodic theory
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Zusammenfassung:We show that any diffeomorphism of a compact manifold can be $C^1$ approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.
ISSN:1435-9855
1435-9863
DOI:10.4171/JEMS/497