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Dehn twists and pseudo-Anosov diffeomorphisms. (English) Zbl 0618.58027
The author shows that it is possible to obtain many pseudo-Anosov diffeomorphisms from Dehn twists. Let M be a closed and oriented surface. The set of isotopy classes of simply connected closed curves on M is denoted by \({\mathcal S}(M)\), the set of isotopy classes of diffeomorphisms by \(\pi_ 0(Diff(M))\). He proves the following theorem: Let f be in \(\pi_ 0(Diff(M))\) and let \(\gamma\) be in \({\mathcal S}(M)\). If the orbit of \(\gamma\) under f fills M, then \(T^ n_{\gamma} f\) is a pseudo-Anosov class except for at most 7 consecutive values of n.
Reviewer: A.Reinfelds (Riga)

MSC:
37D99 Dynamical systems with hyperbolic behavior
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