Local rigidity of partially hyperbolic actions I. KAM method and ℤk actions on the torus

Danijela Damjanovíc, Anatole Katok

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

We show C local rigidity for Z{double-struck}k (k ≥ 2) higher rank partially hyperbolic actions by toral automorphisms, using a generalization of the KAM (Kolmogorov-Arnold-Moser) iterative scheme. We also prove the existence of irreducible genuinely partially hyperbolic higher rank actions on any torus T{double-struck}N for any even N ≥ 6.

Original languageEnglish (US)
Pages (from-to)1805-1858
Number of pages54
JournalAnnals of Mathematics
Volume172
Issue number3
DOIs
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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