Elon Lindenstrauss

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In this paper we present some results and applications of a new invariant for dynamical systems that can be viewed as a dy-namical analogue of topological dimension. This invariant has been introduced by M. Gromov, and enables one to assign a meaningful quantity to dynamical systems of innnite topological dimension and entropy. We also develop an(More)
We study diophantine properties of a typical point with respect to measures on Rn. Namely, we identify geometric conditions on a measure μ on Rn guaranteeing that μ-almost every y ∈ Rn is not very well multiplicatively approximable by rationals. Measures satisfying our conditions are called ‘friendly’. Examples include smooth measures on nondegenerate(More)
as i→∞.) A similar conjecture can be stated also in the finite volume case [6]. Of particular number theoretic interest are manifolds of the form Γ\H with Γ a congruence arithmetic lattice, in which case it is natural to assume that the eigenfunctions are Hecke-Maas forms, i.e. also eigenfunctions of all Hecke operators. We shall refer to this special case(More)
In this paper we give a counter example to a conjecture mentioned in Benjamini and Kesten (1996) about distinguishing sceneries by observing them along a simple random walk, giving an explicit construction of 2 @0 sceneries that are all pairwise indistinguishable.
The main result we prove in this paper is that for any nite dimensional dynamical system (with topological entropy h), and for any factor with strictly lower entropy h 0 , there exist an intermediate factor of entropy h 00 for every h 00 2 h 0 ; h]. Two examples, one of them minimal, show that this is not the case for innnite dimensional systems. The(More)