Geometry & Topology

Unimodal generalized pseudo-Anosov maps

André de Carvalho and Toby Hall

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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.

Article information

Geom. Topol., Volume 8, Number 3 (2004), 1127-1188.

Received: 10 July 2003
Revised: 4 February 2004
Accepted: 1 September 2004
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 57M50: Geometric structures on low-dimensional manifolds

pseudo-Anosov homeomorphisms train tracks unimodal maps horseshoe


de Carvalho, André; Hall, Toby. Unimodal generalized pseudo-Anosov maps. Geom. Topol. 8 (2004), no. 3, 1127--1188. doi:10.2140/gt.2004.8.1127.

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