Homoclinic orbits for area preserving diffeomorphisms of surfaces

We show that $C^r $ generically in the space of $C^r$ conservative diffeomorphisms of a compact surface, every hyperbolic periodic point has a transverse homoclinic orbit.

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2022-03, Vol.42 (3), p.1122-1165
Main Authors: LE CALVEZ, PATRICE, SAMBARINO, MARTÍN
Format: Article
Language:English
Subjects:
Dynamical Systems
Eigenvalues
Entropy
Isomorphism
Mathematics
Orbits
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Description
Summary:We show that $C^r $ generically in the space of $C^r$ conservative diffeomorphisms of a compact surface, every hyperbolic periodic point has a transverse homoclinic orbit.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2021.40