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Homoclinic orbits for area preserving diffeomorphisms of surfaces

Published online by Cambridge University Press:  04 May 2021

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: [email protected])

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.

Type
Original Article
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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