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Invariant rigid geometric structures and expanding maps

Published online by Cambridge University Press:  06 May 2011

YONG FANG
YONG FANG*
Affiliation:
Département de Mathématiques, Université de Cergy-Pontoise, avenue Adolphe Chauvin, 95302, Cergy-Pontoise Cedex, France (email: yfang@math.u-cergy.fr)
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Abstract

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In the first part of this paper, we consider several natural problems about locally homogeneous rigid geometric structures. In particular, we formulate a notion of topological completeness which is adapted to the study of global rigidity of chaotic dynamical systems. In the second part of the paper, we prove the following result: let φ be a C∞ expanding map of a closed manifold. If φ preserves a topologically complete C∞ rigid geometric structure, then φ is C∞ conjugate to an expanding infra-nilendomorphism.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 3 , June 2012 , pp. 941 - 959
Copyright
Copyright © Cambridge University Press 2011

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