zbMATH — the first resource for mathematics

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

37D99 Dynamical systems with hyperbolic behavior
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.