Unimodal generalized pseudo-Anosov maps

DOI10.2140/gt.2004.8.1127zbMath1057.37041arXivmath/0307211OpenAlexW2132015793WikidataQ57740164 ScholiaQ57740164MaRDI QIDQ1882845

André de Carvalho, Toby Hall

Publication date: 1 October 2004

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307211

zbMATH Keywords

horseshoesymbolic dynamicscomplex structureinterval mapsfoliationsunimodal mapstrain tracksPseudo-Anosov homeomorphisms

Mathematics Subject Classification ID

Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) General geometric structures on low-dimensional manifolds (57M50) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Symbolic dynamics (37B10) Dynamical systems involving maps of the interval (37E05) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (10)

Constructing pseudo-Anosov maps with given dilatations ⋮ Laminations and \(2\)-filling rays on infinite type surfaces ⋮ Markov shifts and topological entropy of families of homoclinic tangles ⋮ Typical path components in tent map inverse limits ⋮ Limits of sequences of pseudo-Anosov maps and of hyperbolic 3-manifolds ⋮ Paper folding, Riemann surfaces and convergence of pseudo-Anosov sequences ⋮ Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries ⋮ Paper surfaces and dynamical limits ⋮ Is a typical bi-Perron algebraic unit a pseudo-Anosov dilatation? ⋮ Minimal topological chaos coexisting with a finite set of homoclinic and periodic orbits

Cites Work

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• Topological methods in surface dynamics
• Train-tracks for surface homeomorphisms
• Braid forcing and star-shaped train tracks.
• On the geometry and dynamics of diffeomorphisms of surfaces
• The creation of horseshoes
• Pruning theory and Thurston's classification of surface homeomorphisms

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