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Unimodal generalized
pseudo-Anosov maps
André de Carvalho and Toby Hall |
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Geometry & Topology 8 (2004) 1127–1188
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arXiv: math.DS/0307211 |
Abstract |
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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. |
Keywords
pseudo-Anosov homeomorphisms, train tracks, unimodal maps,
horseshoe
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Mathematical Subject Classification 2000
Primary: 37E30
Secondary: 57M50
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References |
Forward citations |
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
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Authors |
| André de Carvalho | |
| Departamento de Matemática
Aplicada IME - USP Rua do Matão 1010 Cidade Universitária 05508-090 São Paulo São Paulo Brazil |
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| Toby Hall | |
| Department of Mathematical
Sciences University of Liverpool Liverpool L69 7ZL United Kingdom |
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