Coding of closed geodesics after gauss and morse

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Abstract

Closed geodesics associated to conjugacy classes of hyperbolic matrices in SL(2, ℤ) can be coded in two different ways. The geometric code, with respect to a given fundamental region, is obtained by a construction universal for all Fuchsian groups, while the arithmetic code, given by '-' continued fractions, comes from the Gauss reduction theory and is specific for SL(2, ℤ). In this paper we give a complete description of all closed geodesics for which the two codes coincide.

Original languageEnglish (US)
Pages (from-to)123-145
Number of pages23
JournalGeometriae Dedicata
Volume63
Issue number2
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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