TY - JOUR
T1 - Local rigidity of actions of higher rank abelian groups and KAM method
AU - Damjanovi Ć, Danijela
AU - Katok, Anatole
PY - 2004/12/24
Y1 - 2004/12/24
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=15944376276&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=15944376276&partnerID=8YFLogxK
U2 - 10.1090/S1079-6762-04-00139-8
DO - 10.1090/S1079-6762-04-00139-8
M3 - Article
AN - SCOPUS:15944376276
SN - 1079-6762
VL - 10
SP - 142
EP - 154
JO - Electronic Research Announcements of the American Mathematical Society
JF - Electronic Research Announcements of the American Mathematical Society
IS - 16
ER -