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Journal d’Analyse Mathématique

, Volume 81, Issue 1, pp 35–64 | Cite as

Fractions continues sur les surfaces de Veech

  • Pierre Arnoux
  • Pascal Hubert
Article

Abstract

We define a geometrical continued fraction algorithm in the setting of regular polygons with an even number of sides., The definition of the algorithm uses linear transformations generating a group conjugated to an index 2 subgroup of a Hecke group. We give Markov conditions allowing the iteration of the algorithm. We compute the natural extension and the invariant measure for each of the additive and multiplicative versions of this algorithm.

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Copyright information

© Hebrew University of Jerusalem 2000

Authors and Affiliations

  • Pierre Arnoux
    • 1
  • Pascal Hubert
    • 1
  1. 1.Institut de Mathématiques de LuminyMarseille Cedex 9France

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