Backward continued fractions, Hecke groups and invariant measures for transformations of the interval

DOI10.1017/S0143385700010014zbMath0884.58040MaRDI QIDQ5284768

Andrew Haas, Karlheinz Gröchening

Publication date: 15 June 1997

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

zbMATH Keywords

geodesic flowsymbolic dynamicsbackward continued fractionsHecke-type group

Mathematics Subject Classification ID

General groups of measure-preserving transformations (28D15) Geodesic flows in symplectic geometry and contact geometry (53D25) Ergodic theory (37A99) Low-dimensional dynamical systems (37E99) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items

Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics ⋮ Metrical diophantine approximation for continued fraction like maps of the interval ⋮ Haas-Molnar continued fractions and metric Diophantine approximation ⋮ Distribution of approximants and geodesic flows ⋮ A dependence with complete connections approach to generalized Rényi continued fractions ⋮ Two asymptotic distributions related to Rényi-type continued fraction expansions ⋮ Convergence rate for Rényi-type continued fraction expansions ⋮ A Gauss–Kuz’min–Lévy theorem for Rényi-type continued fractions ⋮ Multifractal analysis of the Lyapunov exponent for the backward continued fraction map ⋮ ON BINARY QUADRATIC FORMS AND THE HECKE GROUPS ⋮ Continued fractions on the Veech surfaces

Cites Work

• Unnamed Item
• Transformations on [0,1 with infinite invariant measures]
• Markov maps associated with Fuchsian groups
• Metrical theory for a class of continued fraction transformations and their natural extensions
• Symbolic dynamics for geodesic flows
• Ergodische Theorie von Ziffernentwicklungen in Wahrscheinlichkeitsräumen. (Metrische Zahlentheorie). (Ergodic theory of digit expansions in random spaces)
• Representation of ergodic flows
• A class of continued fractions associated with certain properly discontinuous groups
• Representations for real numbers and their ergodic properties
• The Modular Surface and Continued Fractions
• The backward continued fraction map and geodesic flow
• The Hurwitz Constant and Diophantine Approximation on Hecke Groups
• Geodesic flows, interval maps, and symbolic dynamics
• Backward Continued Fractions and their Invariant Measures
• Ergodic Properties of Linear Fractional Transformations Mod One