Geometry & Topology
- Geom. Topol.
- Volume 8, Number 3 (2004), 1127-1188.
Unimodal generalized pseudo-Anosov maps
An infinite family of generalized pseudo-Anosov homeomorphisms of the sphere 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 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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 57M50: Geometric structures on low-dimensional manifolds
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. https://projecteuclid.org/euclid.gt/1513883464