Coding of closed geodesics after Gauss and Morse

DOI10.1007/BF00148213zbMath0884.20030OpenAlexW2001459503MaRDI QIDQ1815257

Svetlana Katok

Publication date: 31 March 1998

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00148213

zbMATH Keywords

Fuchsian groupsarithmetic codesfundamental regionscodes of closed geodesicsconjugacy classes of hyperbolic matricesgeometry codes

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

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Applications of (a,b)-continued fraction transformations ⋮ Geometric invariants for real quadratic fields ⋮ Values of modular functions at real quadratics and conjectures of Kaneko ⋮ Farey boat: continued fractions and triangulations, modular group and polygon dissections ⋮ On the topological entropy of (a, b)-continued fraction transformations ⋮ Concentration of closed geodesics in the homology of modular curves ⋮ Error approximation for backwards and simple continued fractions ⋮ Phase transitions for suspension flows ⋮ Versions of the closing lemma for certain dynamical systems on tori ⋮ Continued fractions with $SL(2, Z)$-branches: combinatorics and entropy ⋮ A new method of coding geodesics on surfaces whose fundamental regions consist of the union of elementary triangles derived from the Farey series ⋮ On periodicity of geodesic continued fractions ⋮ Extremal parameters and their duals for boundary maps associated to Fuchsian groups ⋮ -DEFORMED RATIONALS AND -CONTINUED FRACTIONS ⋮ Kronecker's first limit formula, revisited ⋮ Topological conjugacy of linear endomorphisms of the 2-torus ⋮ Symbolic dynamics for the modular surface and beyond ⋮ Necessary and sufficient conditions for convergence of integer continued fractions

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