Diagonal changes for surfaces in hyperelliptic components - A geometric natural extension of Ferenczi-Zamboni moves

Vincent Delecroix, Corinna Ulcigrai*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)

Abstract

We describe geometric algorithms that generalize the classical continued fraction algorithm for the torus to all translation surfaces in hyperelliptic components of translation surfaces. We show that these algorithms produce all saddle connections which are best approximations in a geometric sense, which generalizes the notion of best approximation for the classical continued fraction. In addition, they allow to list all systoles along a Teichmueller geodesic and all bispecial words which appear in the symbolic coding of linear flows. The elementary moves of the described algorithms provide a geometric invertible extension of the renormalization moves introduced by S. Ferenczi and L. Zamboni for the corresponding interval exchange transformations.

Original languageEnglish
Pages (from-to)117–174
Number of pages58
JournalGeometriae Dedicata
Volume176
Issue number1
Early online date23 Feb 2014
DOIs
Publication statusPublished - Jun 2015

Keywords

  • Best approximations
  • Continued fraction algorithm
  • Flat systoles
  • Translation surfaces

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