SELF-INVERSES, LAGRANGIAN PERMUTATIONS AND MINIMAL INTERVAL EXCHANGE TRANSFORMATIONS WITH MANY ERGODIC MEASURES

DOI10.1142/S0219199713500193zbMath1345.37037arXiv1202.4035MaRDI QIDQ5401606

Jonathan Fickenscher

Publication date: 10 March 2014

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.4035

zbMATH Keywords

interval exchange transformationTeichmüller geodesic flowmoduli space of abelian differentialsRauzy class

Mathematics Subject Classification ID

Dynamical systems involving maps of the interval (37E05) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (5)

A combinatorial proof of the Kontsevich-Zorich-Boissy classification of Rauzy classes ⋮ Teichmüller dynamics and unique ergodicity via currents and Hodge theory ⋮ Topological mixing for some residual sets of interval exchange transformations ⋮ The number of ergodic measures for transitive subshifts under the regular bispecial condition ⋮ Cohomological equations for linear involutions

Cites Work

• Moduli spaces of quadratic differentials
• Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials
• Gauss measures for transformations on the space of interval exchange maps
• Interval exchange transformations and measured foliations
• Non-ergodic interval exchange transformations
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Deviation of ergodic averages for area-preserving flows on surfaces of higher genus
• The Metric Theory of Interval Exchange Transformations I. Generic Spectral Properties
• The Metric Theory of Interval Exchange Transformations II. Approximation by Primitive Interval Exchanges
• The cohomological equation for Roth-type interval exchange maps
• Decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichmüller flow on the moduli space of Abelian differentials
• Interval exchange transformations
• Interval exchange transformations

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