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Sur une notion d'autonomie de systèmes dynamiques, appliquée aux ensembles invariants des flots d' Anosov algébriques

Published online by Cambridge University Press:  19 September 2008

A. Zeghib
A. Zeghib
Affiliation:
CNRS: UMR 128, Ecole Normale Supérieure de Lyon, 46, Allée d' Italie, 69364 LYON Cedex 07, France
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Abstract

We introduce a notion of autonomous dynamical systems which generalizes algebraic dynamical systems. We show by giving examples and by describing some properties that this generalization is not a trivial one. We apply the methods then developed to algebraic Anosov systems. We prove that a C1-submanifold of finite volume, which is invariant by an algebraic Anosov system is ‘essentially’ algebraic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 1 , February 1995 , pp. 175 - 207
Copyright
Copyright © Cambridge University Press 1995

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