Mixing for smooth time-changes of general nilflows

Artur Avila, Giovanni Forni, Davide Ravotti, Corinna Ulcigrai

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

We consider completely irrational nilflows on any nilmanifold of step at least 2. We show that there exists a dense set of smooth time-changes such that any time-change in this class which is not measurably trivial gives rise to a mixing nilflow. This in particular reproves and generalizes to any nilflow (of step at least 2) the main result proved in [3] for the special class of Heisenberg (step 2) nilflows, and later generalized in [58] to a class of nilflows of arbitrary step which are isomorphic to suspensions of higher-dimensional linear toral skew-shifts.

Original languageEnglish
Article number107759
Number of pages65
JournalAdvances in Mathematics
Volume385
DOIs
Publication statusPublished - 16 Jul 2021

Keywords

  • Mixing
  • Nilflows
  • Parabolic dynamics
  • Time-changes

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