Geometry & Topology, Vol. 8 (2004) Paper no. 31, pages 1127--1188.

Unimodal generalized pseudo-Anosov maps

Andre de Carvalho, Toby Hall

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

AMS subject classification. Primary: 37E30. Secondary: 57M50.

DOI: 10.2140/gt.2004.8.1127

E-print: arXiv:math.DS/0307211

Submitted to GT on 10 July 2003. (Revised 4 February 2004.) Paper accepted 1 September 2004. Paper published 8 September 2004.

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Andre de Carvalho, Toby Hall
Departamento de Matematica Aplicada, IME-USP
Rua do Matao 1010, Cidade Universitaria
05508-090 Sao Paulo, SP, Brazil
and
Department of Mathematical Sciences, University of Liverpool
Liverpool L69 7ZL, UK

Email: andre@ime.usp.br, T.Hall@liv.ac.uk

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