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Analytic models of pseudo-Anosov maps. (English) Zbl 0608.58035
A pseudo-Anosov map is a homeomorphism of a compact surface which is locally of the form \(z\to h(z^{p/2})^{2/p}+z_ 0\), where \(h(x,y)=(\lambda x,y/\lambda)\) for a fixed \(\lambda >1\) and where the integer p depends on the point considered. In particular, a pseudo-Anosov map is a diffeomorphism outside of finitely many singular points. M. Gerber proved that a pseudo-Anosov map f can be approximated by an analytic diffeomorphism which is topologically conjugated to f [Mem. Am. Math. Soc. 321 (1985; Zbl 0572.58018)]. The authors give a new proof of this result.
Reviewer: F.Bonahon

MSC:
37D99 Dynamical systems with hyperbolic behavior
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
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