Geometry & Topology 8 (2004) 1127–1188

DOI: 10.2140/gt.2004.8.1127

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

Primary: 37E30

Secondary: 57M50

References

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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