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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
Keywords:
pseudo-Anosov diffeomorphisms
Full Text:
References:
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