Cascades in the dynamics of affine interval exchange transformations

DOI10.1017/etds.2018.141zbMath1448.37047arXiv1701.02332OpenAlexW2575274091MaRDI QIDQ3298417

Selim Ghazouani, A. Boulanger, Charles Fougeron

Publication date: 14 July 2020

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

Full work available at URL: https://arxiv.org/abs/1701.02332

zbMATH Keywords

topological dynamicsTeichmüller dynamicslow-dimensional dynamics

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) General geometric structures on low-dimensional manifolds (57M50) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems involving maps of the interval (37E05) Flows on surfaces (37E35) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (6)

Internal-wave billiards in trapezoids and similar tables ⋮ Teichmüller dynamics, dilation tori and piecewise affine circle homeomorphisms ⋮ Moduli spaces of complex affine and dilation surfaces ⋮ Dilation surfaces and their Veech groups ⋮ Angels' staircases, Sturmian sequences, and trajectories on homothety surfaces ⋮ Horizon saddle connections, quasi-Hopf surfaces and Veech groups of dilation surfaces

Cites Work

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• Affine interval exchange maps with a wandering interval
• Persistence of wandering intervals in self-similar affine interval exchange transformations
• On the geometry and dynamics of diffeomorphisms of surfaces
• Affine interval exchange transformations with wandering intervals
• Piece-wise affine maps conjugate to interval exchanges
• Dynamique générique des feuilletages transversalement affines des surfaces
• FUNDAMENTAL POLYHEDRONS AND LIMIT POINT SETS OF KLEINIAN GROUPS
• On structural stability

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