Volume 8, issue 3 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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
Mathematical Subject Classification 2000
Primary: 37E30
Secondary: 57M50
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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