A NOTE ON DOUBLE ROTATIONS OF INFINITE TYPE

M. Artigiani, C. Fougeron, P. Hubert, A. Skripchenko

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic.

Original languageEnglish
Pages (from-to)157-172
Number of pages16
JournalTransactions of the Moscow Mathematical Society
Volume82
DOIs
Publication statusPublished - 2021
Externally publishedYes

Keywords

  • Interval translation mappings
  • Rauzy induction
  • unique ergodicity

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