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Difféomorphismes pseudo-Anosov et automorphismes symplectiques de l’homologie. (French) Zbl 0539.58023

Given any surface-diffeomorphism, \(h: M^ 2\to M^ 2\) (genus \(M^ 2\geq 2)\), together with some pseudo-Anosov-diffeomorphism, f, of the same surface. The author then shows that, for almost all \(n\geq 0\), the product \(f^ nh\) is a pseudo-Anosov-diffeomorphism. To prove this result a metric on the (projective) space, P\({\mathfrak MF}\), of all measured foliations on \(M^ 2\) is described and utilized for the action of surface-diffeomorphisms on P\({\mathfrak MF}\). It is known that the product of two appropriate Dehn-twists gives a pseudo-Anosov-diffeomorphism which acts trivially on the homology. Taking this particular diffeomorphism as f, the author obtains as corollary that for any surface-diffeomorphism there is a pseudo-Anosov-diffeomorphism with the same action on the homology.
Reviewer: K.Johannson

MSC:

37D99 Dynamical systems with hyperbolic behavior
57R50 Differential topological aspects of diffeomorphisms
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
57R30 Foliations in differential topology; geometric theory
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References:

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