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Homoclinic orbits for area preserving diffeomorphisms of surfaces

Part of: Low-dimensional dynamical systems Smooth dynamical systems: general theory

Published online by Cambridge University Press:  04 May 2021

PATRICE LE CALVEZ  and
MARTÍN SAMBARINO
PATRICE LE CALVEZ*
Affiliation:
Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG, Sorbonne Université, Université Paris-Diderot, CNRS, F-75005, Paris, France Institut Universitaire de France, 1 rue Descartes, 75231Paris Cedex 05, France
MARTÍN SAMBARINO
Affiliation:
CMAT, Facultad de Ciencias, Universidad de la República, Montevideo11400, Uruguay (e-mail: samba@cmat.edu.uy)
*
e-mail: patrice.le-calvez@imj-prg.fr
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Abstract

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.

Keywords

low dimensional dynamicssmooth dynamicsHamiltonian dynamichomoclinic intersections

MSC classification

Primary: 37C20: Generic properties, structural stability 37C25: Fixed points, periodic points, fixed-point index theory 37C29: Homoclinic and heteroclinic orbits 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 3: Anatole Katok Memorial Issue Part 2: Special Issue of Ergodic Theory and Dynamical Systems , March 2022 , pp. 1122 - 1165
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

In the memory of Anatole Katok

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