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Pré-Publication, Document De Travail Année : 2013

An uncountable family of pairwise non-Kakutani equivalent smooth diffeomorphisms

Résumé

We construct an uncountable family of smooth ergodic zero-entropy di ffeomorphisms that are pairwise non-Kakutani equivalent, on any smooth compact connected manifold of dimension greater than two, on which there exists an effective smooth circle action preserving a positive smooth volume. To that end, we first construct a smooth ergodic zero-entropy and non-Loosely Bernoulli di ffeomorphism, by suitably modifying a smooth construction by Anosov and Katok. A construction of this kind was announced by Katok in 1977 and 1980.
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Dates et versions

hal-00795683 , version 1 (01-03-2013)

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  • HAL Id : hal-00795683 , version 1

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Mostapha Benhenda. An uncountable family of pairwise non-Kakutani equivalent smooth diffeomorphisms. 2013. ⟨hal-00795683⟩
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