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

Danijela Damjanovi Ć; Anatole Katok

doi:10.1090/S1079-6762-04-00139-8

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

Danijela Damjanovi Ć
, Anatole Katok

Research output: Contribution to journal › Article › peer-review

17 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 ℤ^k (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 T^N for any even N ≥ 6.

Original language	English (US)
Pages (from-to)	142-154
Number of pages	13
Journal	Electronic Research Announcements of the American Mathematical Society
Volume	10
Issue number	16
DOIs	https://doi.org/10.1090/S1079-6762-04-00139-8
State	Published - Dec 24 2004

All Science Journal Classification (ASJC) codes

General Mathematics

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AB - 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.

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

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