Danijela Damjanovic, Anatole Katok
Abstract. We consider the restriction α0,G of the Weyl chamber flow on SL(n, R)/Γ (where Γ is a cocompact lattice) to a closed subgroup G isomorphic to Z k × R l, k + l ≥ 2 of the group D+ of...
1 LOCAL RIGIDITY OF PARTIALLY HYPERBOLIC ACTIONS I. KAM METHOD AND Z k ACTIONS ON THE TORUS (2009)
Danijela Damjanovic, Anatole Katok
ABSTRACT. We show C ∞ local rigidity for Z k (k ≥ 2) higherrank partially hyperbolic actions by toral automorphisms, using a generalization of the KAM (Kolmogorov-Arnold-Moser) iterative scheme....
Periodic cycle functionals and Cocycle rigidity for certain partially hyperbolic R k actions (2009)
Danijela Damjanovic, Anatole Katok
Abstract. We give a proof of cocycle rigidity in Hölder and smooth categories for Cartan actions on SL(n, R)/Γ and SL(n, C)/Γ for n ≥ 3 and Γ cocompact lattice, and for restrictions of those...