Geodesic length spectrum on compact Riemann surfaces
type: Item
instance of: scholarly article
title: Geodesic length spectrum on compact Riemann surfaces
zbMATH Open document ID: 1202.37033
author: Clara Gracio
author: J. Sousa Ramos
published in: Journal of Geometry and Physics
publication date: 2010-09-24T00:00:00Z
review text: The variation of the geodesic length spectrum of a compact Riemannian surface of genus 2 is studied via Fenchel-Nielsen coordinates, the structure of Fuchsian groups and Markov symbolic dynamics on the boundary of the Poincaré model of the Lobachevsky geometry. Basing on the correspondence between the geometry of the surface and the algebraic structure of the fundamental group, a precise relation between closed geodesics and periodic sequences in the symbolic system is deduced. This yields a way to compute the length spectra and implies formulae for exponential growth rate of the fundamental group with a particular choice of the generators and the first terms of the growth series.
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 37F30
zbMATH DE Number: 5791202
zbMATH Keywords: geodesic length spectrum
zbMATH Keywords: hyperbolic geometry
zbMATH Keywords: fundamental group of a surface
zbMATH Keywords: Fuchsian group
zbMATH Keywords: Markov symbolic system
reviewed by: Boris Kruglikov
MaRDI profile type: Publication
full work available at URL: j.geomphys.2010.06.006
OpenAlex ID: W2005026228
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DOI: 10.1016/J.GEOMPHYS.2010.06.006
description: scientific article; zbMATH DE number 5791202