Templates for geodesic flows

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8 Scopus citations

Abstract

We construct templates for geodesic flows on an infinite family of Hecke triangle groups. Our results generalize those of E. Ghys [Knots and dynamics. Proc. Int. Congress of Mathematicians. Vol. 1. International Congress of Mathematicians, Zürich, 2007], who constructed a template for the modular flow in the complement of the trefoil knot in S3. A significant difficulty that arises in any attempt to go beyond the modular flow is the fact that for other Hecke triangles the geodesic flow cannot be viewed as a flow in S3, and one is led to consider embeddings into lens spaces. Our final result is an explicit description of a single 'Hecke template' which contains all other templates we construct, allowing a topological study of the periodic orbits of different Hecke triangle groups all at once.

Original languageEnglish
Pages (from-to)211-235
Number of pages25
JournalErgodic Theory and Dynamical Systems
Volume34
Issue number1
DOIs
StatePublished - 2014

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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