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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)
##### Keywords:
pseudo-Anosov map; analytic diffeomorphism
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##### References:
 [1] DOI: 10.2307/1971237 · Zbl 0435.58021 · doi:10.2307/1971237 [2] Gerber, Ann. Scient. Ec. Norm. Sup. 15 pp 173– (1982) [3] Gerber, Mem. Amer. Math. Soc. 54 pp 321– (1985) [4] Fathi, Asterisque none pp 66– (1979) [5] Katok, Constructions in Ergodic Theory [6] DOI: 10.2307/1994022 · Zbl 0141.19407 · doi:10.2307/1994022 [7] Lewowicz, Ergod. Th. & Dynam. Sys. 3 pp 567– (1983) [8] DOI: 10.1016/0022-0396(80)90004-2 · Zbl 0418.58012 · doi:10.1016/0022-0396(80)90004-2 [9] DOI: 10.1070/RM1977v032n04ABEH001639 · Zbl 0383.58011 · doi:10.1070/RM1977v032n04ABEH001639
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