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Construction d'un difféomorphisme minimal d'entropie topologique non nulle

Published online by Cambridge University Press:  19 September 2008

M. R. Herman
M. R. Herman*
Affiliation:
Centre de Mathématiques de l'Ecole Polytechnique, Palaiseau, France
*
†M. R. Herman, Centre de Mathématiques de l'Ecole Polytechnique, Plateau de Palaiseau, 91128 Palaiseau Cedex, France.
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Abstract

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We construct a real analytic diffeomorphism Fα on a compact connected 4-dimensional manifold M, such that Fα preserves a probability measure μ defined by a smooth volume form, Fα is a minimal diffeomorphism of M and furthermore the metrical entropy of Fα with respect to the measure μ is strictly positive. By a theorem of Goodwyn the topological entropy is also strictly positive. We write down the explicit formula of Fα that depends on a parameter α ∈ T1. This parameter is chosen by Baire category.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 1 , March 1981 , pp. 65 - 76
Copyright
Copyright © Cambridge University Press 1981

References

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