Measurable Distal and Topological Distal Systems (2008)
In this paper we prove that any ergodic measurably distal system can be realized as a minimal topologically distal system with an invariant Borel measure of full support. The proof depends upon a...
Ergodic Theory of the Space of Measured Laminations (2008)
Lindenstrauss, Elon, Mirzakhani, Maryam
We classify locally finite invariant measures and orbit closure for the action of the mapping class group on the space of measured laminations on a surface. This classification translates to a...
Mean topological dimension (2007)
Elon Lindenstrauss, Benjamin Weiss
Abstract. In this paper we present some results and applications of a new invariant for dynamical systems that can be viewed as a dynamical analogue of topological dimension. This invariant has been...
Mean dimension, small entropy factors and an imbedding theorem, preprint (2007)
Abstract. In this paper we show how the notion of mean dimension is connected in a natural way to the following two questions: what points in a dynamical system (X; T) can be distinguished by factor...
Elon Lindenstrauss, David Meiri, Yuval Peres, P N \gamma
Abstract. Given ergodic p-invariant measures f i g on the 1-torus T = R=Z, we give a sharp condition on their entropies, guaranteeing that the entropy of the convolution 1 \Delta \Delta \Delta n...
Distribution of periodic torus orbits and Duke's theorem for cubic fields (2007)
Einsiedler, Manfred, Lindenstrauss, Elon, Michel, Philippe, Venkatesh, Akshay
We study periodic torus orbits on spaces of lattices. Using the action of the group of adelic points of the underlying tori, we define a natural equivalence relation on these orbits, and show that...
Invariant measures and the set of exceptions to Littlewood's conjecture (2006)
Einsiedler, Manfred, Katok, Anatole, Lindenstrauss, Elon
We classify the measures on SL (k,R)/SL (k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set...
Invariant measures and the set of exceptions to Littlewood's conjecture (2006)
Ensiedler, Manfred, Katok, Anatole, Lindenstrauss, Elon
We classify the measures on $\SL (k,\Bbb R) / \SL (k, \ZZ)$ which are invariant and ergodic under the action of the group $A$ of positive diagonal matrices with positive entropy. We apply this to...
The distribution of periodic torus orbits on homogeneous spaces (2006)
Einsiedler, Manfred, Lindenstrauss, Elon, Michel, Philippe, Venkatesh, Akshay
We prove results towards the equidistribution of certain families of periodic torus orbits on homogeneous spaces, with particular focus on the case of the diagonal torus acting on quotients of...
Invariant measures and arithmetic quantum unique ergodicity (2006)
We classify measures on the locally homogeneous space $\Gamma\backslash \SL ( 2 , \R ) \times L$ which are invariant and have positive entropy under the diagonal subgroup of $\SL ( 2 , \R )$ and...
Invariant measures and arithmetic unique ergodicity (2006)
We classify measures on the locally homogeneous space ¿¡\ SL(2,R) ¿~ L which are invariant and have positive entropy under the diagonal subgroup of SL(2,R) and recurrent under L. This...
Invariant measures and the set of exceptions to Littlewood's conjecture (2006)
Einsiedler, Manfred, Katok, Anatole, Lindenstrauss, Elon
We classify the measures on SL (k,R)/SL (k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set...
Existence and Weyl's law for spherical cusp forms (2005)
Lindenstrauss, Elon, Venkatesh, Akshay
Let G be a split adjoint semisimple group over Q and K a maximal compact subgroup of the real points G(R). We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp...
Symbolic representations of nonexpansive group automorphisms (2004)
Lindenstrauss, Elon, Schmidt, Klaus
If $\alpha $ is an irreducible nonexpansive ergodic automorphism of a compact abelian group $X$ (such as an irreducible nonhyperbolic ergodic toral automorphism), then $\alpha $ has no finite or...
Rigidity of multiparameter actions (2004)
We survey some recent developments and applications of the study of the rigidity properties of natural algebraic actions of multidimensional abelian groups.
Invariant sets and measures of nonexpansive group automorphisms (2003)
Lindenstrauss, Elon, Schmidt, Klaus
We prove that the restriction of a probability measure invariant under a nonhyperbolic, ergodic and totally irreducible automorphism of a compact connected abelian group to the leaves of the central...
The Erwin, Schrödinger International Boltzmanngasse, Elon Lindenstrauss, Klaus Schmidt, Elon Lindenstrauss, Klaus Schmidt
Abstract. We prove that the restriction of a probability measure invariant under a nonhyperbolic, ergodic and totally irreducible automorphism of a compact connected abelian group to the leaves of...
On the projections of measures invariant under the geodesic flow (2003)
Ledrappier, François, Lindenstrauss, Elon
We consider general probability measures μ on SM, the unit tangent bundle of a Riemannian surface M, invariant under the geodesic flow, and study their projection to M. We show that if dim μ ≤...
Entropy of convolutions on the circle (1999)
Lindenstrauss, Elon, Meiri, David, Peres, Yuval
Given ergodic p-invariant measures {\mu_i} on the 1-torus T=R/Z, we give a sharp condition on their entropies, guaranteeing that the entropy of the convolution \muon converges to \log p. We also...
Indistinguishable sceneries (1999)
Abstract. 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...
Entropy Of Convolutions On The Circle (1997)
Elon Lindenstrauss, David Meiri, Yuval Peres, P N \gamma
. Given ergodic p-invariant measures f¯ i g on the 1-torus T = R=Z, we give a sharp condition on their entropies, guaranteeing that the entropy of the convolution ¯ 1 \Delta \Delta \Delta ¯n...
Lowering Topological Entropy (1995)
The main result we prove in this paper is that for any finite dimensional dynamical system (with topological entropy h), and for any factor with strictly lower entropy h 0 , there exist an...