#### Volume 8, issue 3 (2004)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear 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
Primary: 37E30
Secondary: 57M50