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Unimodal generalized pseudo-Anosov maps

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Bibliographic Details
Title:	Unimodal generalized pseudo-Anosov maps
Authors:	de Carvalho, André, Hall, Toby
Source:	Geom. Topol. 8, no. 3 (2004), 1127-1188
Publication Status:	Preprint
Publisher Information:	Mathematical Sciences Publishers, 2004.
Publication Year:	2004
Subject Terms:	37E30, interval maps, Dynamical Systems (math.DS), 01 natural sciences, Mathematics - Geometric Topology, train tracks, symbolic dynamics, unimodal maps, General geometric structures on low-dimensional manifolds, FOS: Mathematics, Dynamical aspects of holomorphic foliations and vector fields, Mathematics - Dynamical Systems, 0101 mathematics, foliations, Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.), Pseudo-Anosov homeomorphisms, pseudo-Anosov homeomorphisms, Symbolic dynamics, Geometric Topology (math.GT), Small divisors, rotation domains and linearization in holomorphic dynamics, 37E30, 57M50, 57M50, Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces, Dynamical systems involving maps of the interval, horseshoe, complex structure
Description:	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. Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper31.abs.html
Document Type:	Article Other literature type
File Description:	application/xml; application/pdf
Language:	English
ISSN:	1364-0380 1465-3060
DOI:	10.2140/gt.2004.8.1127
DOI:	10.48550/arxiv.math/0307211
Access URL:	http://msp.org/gt/2004/8-3/gt-v8-n3-p05-s.pdf http://arxiv.org/abs/math/0307211 https://zbmath.org/2105214 https://doi.org/10.2140/gt.2004.8.1127 https://arxiv.org/pdf/math/0307211.pdf https://arxiv.org/abs/math/0307211 http://ui.adsabs.harvard.edu/abs/2003math......7211D/abstract https://msp.org/gt/2004/8-3/gt-v8-n3-p05-s.pdf https://www.msp.org/gt/2004/8-3/p05.xhtml https://www.emis.de/journals/UW/gt/ftp/main/2004/2004l31.pdf http://emis.maths.adelaide.edu.au/journals/UW/gt/ftp/main/2004/2004l31.pdf https://www.bv.fapesp.br/pt/publicacao/49233/unimodal-generalized-pseudo-anosov-maps/ https://core.ac.uk/display/21987113 https://projecteuclid.org/euclid.gt/1513883464
Rights:	arXiv Non-Exclusive Distribution
Accession Number:	edsair.doi.dedup.....272d465e83848b15d7ab452db16a9f2d
Database:	OpenAIRE

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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.<br />Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper31.abs.html
ISSN:	13640380 14653060
DOI:	10.2140/gt.2004.8.1127