Unimodal generalized pseudo-Anosov maps

Details Unimodal generalized pseudo-Anosov maps Unimodal generalized pseudo-Anosov maps

2003-07-15

arxiv.org/abs/math/0307211v2

Geom. Topol. 8(2004) 1127-1188

Mathematics

Dynamical Systems

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper31.abs.html

Scientific paper

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.

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