Geometrical Models for Substitutions

DOI10.1080/10586458.2011.544590zbMath1266.37008OpenAlexW2108446105MaRDI QIDQ4915376

Xavier Bressaud, Pierre Arnoux, Julien Bernat

Publication date: 10 April 2013

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1317924392

zbMATH Keywords

Rauzy fractalsinterval exchange transformationsPeano curvessubstitutive dynamical systems

Mathematics Subject Classification ID

Symbolic dynamics (37B10) Dynamical systems involving maps of the interval (37E05)

Related Items (12)

New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant ⋮ Triangle Tiling Billiards and the Exceptional Family of their Escaping Trajectories: Circumcenters and Rauzy Gasket ⋮ Deviation of ergodic averages for substitution dynamical systems with eigenvalues of modulus 1 ⋮ Arnoux-Rauzy interval exchanges ⋮ Infinitely many lattice surfaces with special pseudo-Anosov maps ⋮ Characterization of minimal sequences associated with self-similar interval exchange maps ⋮ Geometrical models for a class of reducible Pisot substitutions ⋮ Random product of substitutions with the same incidence matrix ⋮ Rigidity of square-tiled interval exchange transformations ⋮ Geometry of the common dynamics of Pisot substitutions with the same incidence matrix ⋮ Wandering intervals in affine extensions of self-similar interval exchange maps: the cubic Arnoux–Yoccoz map ⋮ Self-similar sets satisfying the common point property

Cites Work

• Two-dimensional iterated morphisms and discrete planes
• Substitutions in dynamics, arithmetics and combinatorics
• The Arnoux-Yoccoz Teichmüller disc
• Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions
• Veech groups without parabolic elements
• Interval exchange transformations over algebraic number fields: the cubic Arnoux–Yoccoz model
• Some compact invariant sets for hyperbolic linear automorphisms of torii
• Identifications and Dimension of the Rauzy Fractal
• Geodesic laminations as geometric realizations of Pisot substitutions
• Higher dimensional extensions of substitutions and their dual maps

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