Invariant distributions for homogeneous flows and affine transformations

Livio Flaminio, Giovanni Forni, Federico Rodriguez Hertz

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a torus. We also prove that the same conclusion holds for every affine transformation of a homogenous space which is not conjugate to a toral translation. As a part of the proof, we have that any smooth partially hyperbolic flow on any compact manifold has countably many distinct minimal sets, hence countably many distinct ergodic probability measures. As a consequence, the Katok and Greenfield-Wallach conjectures hold in all of the above cases.

Original languageEnglish (US)
Pages (from-to)33-79
Number of pages47
JournalJournal of Modern Dynamics
Volume10
DOIs
StatePublished - Mar 22 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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