Coding of closed geodesics after gauss and morse

Research output: Contribution to journalArticle

23 Citations (Scopus)

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

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Closed Geodesics
Gauss
Coding
Fuchsian Group
Conjugacy class
Continued fraction

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

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Coding of closed geodesics after gauss and morse. / Katok, Svetlana.

In: Geometriae Dedicata, Vol. 63, No. 2, 01.01.1996, p. 123-145.

Research output: Contribution to journalArticle

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