Invariant Measures and the Set of Exceptions to Littlewood's Conjecture Page 1 Annals of
Mathematics, 164 (2006), 513-560 Invariant measures and the set of exceptions to Littlewood's …

Let {gt} be a nonquasiunipotent one-parameter subgroup of a connected semisimple Lie
group G without compact factors; we prove that the set of points in a homogeneous space …

We consider a large class of partially hyperbolic systems containing, among others, affine
maps, frame flows on negatively curved manifolds, and mostly contracting diffeomorphisms …

Consider a smooth one-parameter family t-> f_t of dynamical systems f_t, with| t|< epsilon.
Assume that for all t (or for many t close to t= 0) the map f_t admits a unique SRB invariant …

Consider a one parameter family of diffeomorphisms f ε such that f 0 is an Anosov element in
a standard abelian Anosov action having sufficiently strong mixing properties. Let ν ε be any …

Invariant measures for higher-rank hyperbolic abelian actions Page 1 Ergod. Th. & Dynam. Sys.
(1996), 16, 751-778 Printed in Great Britain Copyright © Cambridge University Press Invariant …

I. Introduction. Throughout the last two or three decades, the theory of rigidity, particularly in
relation to semisimple groups and their discrete subgroups, has become an extremely active …

We show that most homogeneous Anosov actions of higher rank Abelian groups are locally
smoothly rigid (up to an automorphism). This result is the main part in the proof of local …

These are notes for a minicourse in the School on Dynamical Systems 2015 at ICTP. This
version is quite preliminary, incomplete (mainly in the last sections) and probably contains …

Publisher Summary This chapter presents an exposition of homogeneous dynamics—that is,
the dynamical and ergodic properties of actions on the homogeneous spaces of Lie groups …