Applications of (a,b)-continued fraction transformations

DOI10.1017/S0143385711000460zbMath1273.37006arXiv1105.6133OpenAlexW2008853256MaRDI QIDQ2908156

Svetlana Katok, Ilie Ugarcovici

Publication date: 4 September 2012

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

Full work available at URL: https://arxiv.org/abs/1105.6133

zbMATH Keywords

geodesicscontinued fractionsarithmetic codingmodular surfaceBernoulli shifts

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Symbolic dynamics (37B10) Metric theory of continued fractions (11K50) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (9)

Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics ⋮ Structure of attractors for boundary maps associated to Fuchsian groups ⋮ On the topological entropy of (a, b)-continued fraction transformations ⋮ Substitutions, symbolic codings, and discrepancy ⋮ Continued fractions with $SL(2, Z)$-branches: combinatorics and entropy ⋮ Matching in a family of piecewise affine maps ⋮ On certain orbits of geodesic flow and \((a,b)\)-continued fractions ⋮ Extremal parameters and their duals for boundary maps associated to Fuchsian groups ⋮ Tanaka–Ito α-continued fractions and matching

Cites Work

• Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
• Markov maps associated with Fuchsian groups
• Coding of closed geodesics after Gauss and Morse
• Structure and continuity of measurable flows
• Symbolic dynamics for the modular surface and beyond
• Geodesic flows, interval maps, and symbolic dynamics
• Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points
• Symbolic dynamics and Markov partitions
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