Geometry & Topology

Unimodal generalized pseudo-Anosov maps

André de Carvalho and Toby Hall

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Abstract

An infinite family of generalized pseudo-Anosov homeomorphisms of the sphere S is constructed, and their invariant foliations and singular orbits are described explicitly by means of generalized train tracks. The complex strucure induced by the invariant foliations is described, and is shown to make S into a complex sphere. The generalized pseudo-Anosovs thus become quasiconformal automorphisms of the Riemann sphere, providing a complexification of the unimodal family which differs from that of the Fatou/Julia theory.

Article information

Source
Geom. Topol., Volume 8, Number 3 (2004), 1127-1188.

Dates
Received: 10 July 2003
Revised: 4 February 2004
Accepted: 1 September 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513883464

Digital Object Identifier
doi:10.2140/gt.2004.8.1127

Mathematical Reviews number (MathSciNet)
MR2087080

Zentralblatt MATH identifier
1057.37041

Subjects
Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 57M50: Geometric structures on low-dimensional manifolds

Keywords
pseudo-Anosov homeomorphisms train tracks unimodal maps horseshoe

Citation

de Carvalho, André; Hall, Toby. Unimodal generalized pseudo-Anosov maps. Geom. Topol. 8 (2004), no. 3, 1127--1188. doi:10.2140/gt.2004.8.1127. https://projecteuclid.org/euclid.gt/1513883464


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