Cutting sequences on translation surfaces

Diana Davis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We analyze the cutting sequences associated to geodesic flow on a large class of translation surfaces, including Bouw-Möller surfaces. We give a combinatorial rule that relates a cutting sequence corresponding to a given trajectory, to the cutting sequence corresponding to the image of that trajectory under the parabolic element of the Veech group. This extends previous work for regular polygon surfaces to a larger class of translation surfaces. We find that the combinatorial rule is the same as for regular polygon surfaces in about half of the cases, and different in the other half.

Original languageEnglish (US)
Pages (from-to)399-429
Number of pages31
JournalNew York Journal of Mathematics
Volume20
StatePublished - Jan 1 2014

Keywords

  • Geodesics
  • Symbolic dynamics
  • Translation surfaces
  • Veech surfaces

ASJC Scopus subject areas

  • Mathematics(all)

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