Persistence of wandering intervals in self-similar affine interval exchange transformations

DOI10.1017/S0143385709000418zbMath1200.37002arXiv0801.2088MaRDI QIDQ3569983

Pascal Hubert, Alejandro Maass, Xavier Bressaud

Publication date: 22 June 2010

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.2088

zbMATH Keywords

interval exchange transformationsminimal pointswandering setsaffine interval exchange transformation

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Dynamical systems involving maps of the interval (37E05) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (15)

Smooth generalized interval exchange transformations with wandering intervals, from explicit derived from pseudo-Anosov maps ⋮ Deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus 1 ⋮ Teichmüller dynamics, dilation tori and piecewise affine circle homeomorphisms ⋮ Linearization of generalized interval exchange maps ⋮ Order Conditions for Languages ⋮ A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two ⋮ Dynamics and ``arithmetics of higher genus surface flows ⋮ Limit theorems for translation flows ⋮ Cascades in the dynamics of affine interval exchange transformations ⋮ Characterization of minimal sequences associated with self-similar interval exchange maps ⋮ Full families of generalized interval exchange transformations ⋮ Dilation surfaces and their Veech groups ⋮ Wandering intervals in affine extensions of self-similar interval exchange maps: the cubic Arnoux–Yoccoz map ⋮ Dynamical aspects of piecewise conformal maps ⋮ Affine interval exchange transformations with flips and wandering intervals

Cites Work

• Substitutions in dynamics, arithmetics and combinatorics
• La décomposition dynamique et la différentiabilité des feuilletages des surfaces. (The dynamic decomposition and the differentiability of foliations of surfaces)
• Substitution dynamical systems - spectral analysis
• Gauss measures for transformations on the space of interval exchange maps
• Digital sum problems and substitutions on a finite alphabet
• Billiards on rational-angled triangles
• Prefix-suffix automaton associated with a primitive substitution
• Symbolic discrepancy and self-similar dynamics.
• Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
• Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
• Veech groups without parabolic elements
• On the geometry and dynamics of diffeomorphisms of surfaces
• Remarks on the remainder in Birkhoff's ergodic theorem
• Affine interval exchange transformations with wandering intervals
• Bratteli-Vershik models for Cantor minimal systems associated to interval exchange transformations
• Piece-wise affine maps conjugate to interval exchanges
• ORDERED BRATTELI DIAGRAMS, DIMENSION GROUPS AND TOPOLOGICAL DYNAMICS
• The cohomological equation for Roth-type interval exchange maps

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