The scenery flow for geometric structures on the torus: The linear setting

DOI10.1142/S0252959901000425zbMath0993.37018OpenAlexW2100975307MaRDI QIDQ5955015

Pierre Arnoux, Albert Meads Fisher

Publication date: 16 September 2002

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0252959901000425

zbMATH Keywords

continued fractionsSturmian sequencesmodular surfacehorocyclic flowsplane tilingssubstitution dynamical systemTeichmüller flowtranslation flows

Mathematics Subject Classification ID

Teichmüller theory for Riemann surfaces (30F60) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (13)

Dynamical directions in numeration ⋮ A temporal central limit theorem for real-valued cocycles over rotations ⋮ Minimality and unique ergodicity for adic transformations ⋮ Dynamics of Ostrowski skew-product: 1. Limit laws and Hausdorff dimensions ⋮ Multidimensional continued fractions and symbolic codings of toral translations ⋮ Geometry, dynamics, and arithmetic of $S$-adic shifts ⋮ Generalizations of Sturmian sequences associated with \(\boldsymbol{N}\)-continued fraction algorithms ⋮ S-adic Sequences: A Bridge Between Dynamics, Arithmetic, and Geometry ⋮ Recognizability for sequences of morphisms ⋮ Area convergence of Voronoi cells on spiral lattices ⋮ Structure of three-interval exchange transformations. III: Ergodic and spectral properties ⋮ Continued fractions on the Veech surfaces ⋮ Combinatorial, ergodic and arithmetic properties of the Tribonacci substitution

Cites Work

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• Some skew product transformations associated with continued fractions and their invariant measures
• The Teichmüller geodesic flow
• Gauss measures for transformations on the space of interval exchange maps
• Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms
• Minimal cocycles with the scaling property and substitutions
• The Modular Surface and Continued Fractions
• Un exemple de semi-conjugaison entre un échange d'intervalles et une translation sur le tore
• The Metric Theory of Interval Exchange Transformations I. Generic Spectral Properties
• The dynamical properties of Penrose tilings
• Geodesic flows, interval maps, and symbolic dynamics
• Minimal symbolic flows having minimal block growth
• Ratio geometry, rigidity and the scenery process for hyperbolic Cantor sets
• Topological weak-mixing of interval exchange maps
• Ergodic theory and the geodesic flow on surfaces of constant negative curvature
• Sequences with minimal block growth
• A New Proof for a Metrically Transitive System
• Sturmian Minimal Sets

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