Geodesics on modular surfaces and continued fractions

DOI10.1017/S0143385700009585zbMath0497.10007MaRDI QIDQ3960764

Richard Moeckel

Publication date: 1982

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

zbMATH Keywords

ergodicitygeodesic flowsmodular groupRiemann surfacecontinued fractionsmodular surfaces

Mathematics Subject Classification ID

Structure of modular groups and generalizations; arithmetic groups (11F06) Continued fractions (11A55) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (15)

The Erdős–Moser equation $1^{k}+2^{k}+\dots+(m-1)^{k}=m^{k}$ revisited using continued fractions ⋮ Odd-odd continued fraction algorithm ⋮ Hurwitz sequences, the Farey process, and general continued fractions ⋮ Distribution of approximants and geodesic flows ⋮ On word structure of the modular group over finite and real quadratic fields ⋮ On a problem of A. Weil ⋮ A new method of coding geodesics on surfaces whose fundamental regions consist of the union of elementary triangles derived from the Farey series ⋮ Coding of geodesics on some modular surfaces and applications to odd and even continued fractions ⋮ Arithmetic distributions of convergents arising from Jacobi-Perron algorithm ⋮ Some probabilistic results on the convergents of continued fractions ⋮ Tracing compressed curves in triangulated surfaces ⋮ Hermitian continued fractions and hyperbolic billards ⋮ A symbolic dynamics for geodesics on punctured Riemann surfaces ⋮ Symbolic dynamics for the modular surface and beyond ⋮ Geodesic flows and the mother of all continued fractions

Cites Work

• A Metrically Transitive Group Defined by the Modular Groups
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