Weak mixing in interval exchange transformations of periodic type

DOI10.1007/s11005-005-0011-0zbMath1105.37002OpenAlexW2021539628MaRDI QIDQ2583211

Corinna Ulcigrai, Yakov G. Sinai

Publication date: 13 January 2006

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-005-0011-0

zbMATH Keywords

spectral measuresweak mixinginterval exchange transformationsRauzy-Veech cocycle

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Ergodicity, mixing, rates of mixing (37A25) Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems involving maps of the interval (37E05)

Related Items (13)

Smooth generalized interval exchange transformations with wandering intervals, from explicit derived from pseudo-Anosov maps ⋮ Optimal Mixing Enhancement by Local Perturbation ⋮ Optimal linear response for Markov Hilbert-Schmidt integral operators and stochastic dynamical systems ⋮ Quantitative weak mixing for interval exchange transformations ⋮ Cocycles over interval exchange transformations and multivalued Hamiltonian flows ⋮ Dynamics and ``arithmetics of higher genus surface flows ⋮ Ratner’s property and mild mixing for smooth flows on surfaces ⋮ Limit theorems for translation flows ⋮ A generalization of the self-dual induction to every interval exchange transformation ⋮ On the self-similarity problem for smooth flows on orientable surfaces ⋮ Ergodic properties of infinite extensions of area-preserving flows ⋮ On Sarnak's conjecture and Veech's question for interval exchanges ⋮ Unnamed Item

Cites Work

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• Interval exchange transformations and some special flows are not mixing
• Gauss measures for transformations on the space of interval exchange maps
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• Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
• Weak mixing for interval exchange transformations and translation flows
• Échanges d'intervalles et transformations induites
• The Metric Theory of Interval Exchange Transformations I. Generic Spectral Properties
• Deviation for interval exchange transformations
• Substitution dynamical systems : algebraic characterization of eigenvalues
• The cohomological equation for Roth-type interval exchange maps

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