Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation

Christopher Leininger, Anna Lenzhen, Kasra Rafi

Research output: Contribution to journalArticlepeer-review

Abstract

We describe a method for constructing Teichmüller geodesics where the vertical foliation ν is minimal but is not uniquely ergodic and where we have a good understanding of the behavior of the Teichmüller geodesic. The construction depends on various parameters, and we show that one can adjust the parameters to ensure that the set of accumulation points of such a geodesic in the Thurston boundary is exactly the projective 1-simplex of all projective measured foliations that are topologically equivalent to ν. With further adjustment of the parameters, one can further assume that the transverse measure is an ergodic measure on the non-uniquely ergodic foliation ν. 1

Original languageEnglish (US)
JournalJournal fur die Reine und Angewandte Mathematik
Volume2015
DOIs
StatePublished - 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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