Local rigidity of actions of higher rank abelian groups and KAM method

Danijela Damjanovi Ć, Anatole Katok

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

We develop a new method for proving local differentiable rigidity for actions of higher rank abelian groups. Unlike earlier methods it does not require previous knowledge of structural stability and instead uses a version of the KAM (Kolmogorov-Arnold-Moser) iterative scheme. As an application we show C∞ local rigidity for ℤk (k ≥ 2) partially hyperbolic actions by toral automorphisms. We also prove the existence of irreducible genuinely partially hyperbolic higher rank actions by automorphisms on any torus TN for any even N ≥ 6.

Original languageEnglish (US)
Pages (from-to)142-154
Number of pages13
JournalElectronic Research Announcements of the American Mathematical Society
Volume10
Issue number16
DOIs
StatePublished - Dec 24 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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