Volume 8, issue 3 (2004)

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Unimodal generalized pseudo-Anosov maps

André de Carvalho and Toby Hall

Geometry & Topology 8 (2004) 1127–1188
 arXiv: math.DS/0307211
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.

Keywords
pseudo-Anosov homeomorphisms, train tracks, unimodal maps, horseshoe
Primary: 37E30
Secondary: 57M50
Publication
Received: 10 July 2003
Revised: 4 February 2004
Accepted: 1 September 2004
Published: 8 September 2004
Proposed: Joan Birman
Seconded: David Gabai, Yasha Eliashberg
Authors
 André de Carvalho Departamento de Matemática Aplicada IME - USP Rua do Matão 1010 Cidade Universitária 05508-090 São Paulo São Paulo Brazil Toby Hall Department of Mathematical Sciences University of Liverpool Liverpool L69 7ZL United Kingdom