Unimodal generalized pseudo-Anosov maps

de Carvalho, André¹ ; Hall, Toby²

¹ Departamento de Matemática Aplicada, IME - USP, Rua do Matão 1010, Cidade Universitária, 05508-090 São Paulo, São Paulo, Brazil
² Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom

Geometry & topology, Tome 8 (2004) no. 3, pp. 1127-1188.

Résumé

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.

Détail

DOI : 10.2140/gt.2004.8.1127

Keywords: pseudo-Anosov homeomorphisms, train tracks, unimodal maps, horseshoe

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