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Aubry–Mather theory for homeomorphisms

Published online by Cambridge University Press:  05 August 2014

ALBERT FATHI and
PIERRE PAGEAULT
ALBERT FATHI
Affiliation:
Institut universitaire de France, Unité de mathématiques pures et appliquées, CNRS UMR 5669 & École Normale Supérieure de Lyon, 46 allée d’Italie, 69364 Lyon, France email albert. fathi@ens-lyon. fr
PIERRE PAGEAULT
Affiliation:
Unité de mathématiques pures et appliquées, CNRS UMR 5669 & École Normale Supérieure de Lyon, 46 allée d’Italie, 69364 Lyon, France email ppageault@gmail. com
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Abstract

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In this paper, we develop a variational approach to study the dynamic of a homeomorphism on a compact metric space. In particular, we describe orbits along which any Lipschitz Lyapunov function has to be constant via a non-negative Lipschitz semi-distance. We give the link with Auslander’s notion of generalized recurrence, and recover in a different way some parts of a more recent work of Akin and Auslander.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 4 , June 2015, pp. 1187 - 1207
Copyright
© Cambridge University Press, 2014 

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