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Flat surfaces, Bratteli diagrams and unique ergodicity à la Masur

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Abstract

Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of finite area. A criterion of unique ergodicity similar to that of Masur’s for flat surface holds: if there is a subsequence of the renormalizing dynamical system which has a good accumulation point, the translation flow or Bratteli–Vershik transformation is uniquely ergodic. Related questions are explored.

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Authors and Affiliations

  1. Brooklyn College, City University of New York, 2900 Bedford Ave., Brooklyn, NY, 11210, USA

    Rodrigo Treviño

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  1. Rodrigo Treviño
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Correspondence to Rodrigo Treviño.

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Treviño, R. Flat surfaces, Bratteli diagrams and unique ergodicity à la Masur. Isr. J. Math. 225, 35–70 (2018). https://doi.org/10.1007/s11856-018-1636-x

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  • DOI: https://doi.org/10.1007/s11856-018-1636-x

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