Diophantine approximations on fractals (2009)
Einsiedler, Manfred, Fishman, Lior, Shapira, Uri
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle...
The Erwin, Schrödinger International Boltzmanngasse, Manfred Einsiedler, Selim Tuncel
Abstract. We use Gröbner bases and a theorem of Handelman to show that an ideal I of R[x1,..., xk] contains a polynomial with positive coefficients if and only if no initial ideal inv(I), v ∈ R k,...
Invariant measures on G/Γ for split simple Lie groups (2009)
Manfred Einsiedler, Anatole Katok
Abstract. We study the left action α of a Cartan subgroup on the space X = G/Γ, where Γ is a lattice in a simple split connected Lie group G of rank n> 1. Let µ be an α-invariant measure on...
Rigidity of measures – the high entropy case, and non-commuting foliations (2009)
Manfred Einsiedler, Anatole Katok
Abstract. We consider invariant measures for partially hyperbolic, semisimple, higher rank actions on homogeneous spaces defined by products of real and p-adic Lie groups. In this paper we generalize...
Einsiedler, Manfred, Fish, Alexander
We prove that if a Borel probability measure (\mu) on (\T) is invariant under the action of a "large" multiplicative semigroup (lower logarithmic density is positive) and the action of the whole...
ALGEBRAIC Z d-ACTIONS OF ENTROPY RANK ONE (2008)
Manfred Einsiedler, Douglas Lind
Abstract. We investigate algebraic Z d-actions of entropy rankone, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on...
Manfred Einsiedler, Douglas Lind, Richard Miles, Thomas Ward
Abstract. A general framework for investigating topological actions of Z d on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of...
London Mathematical Society ISSN 1461–1570 PRIMES IN ELLIPTIC DIVISIBILITY SEQUENCES (2007)
Morgan Ward pursued the study of elliptic divisibility sequences initiated by Lucas, and Chudnovsky and Chudnovsky suggested looking at elliptic divisibility sequences for prime appearance. The...
Asymptotic geometry of non-mixing sequences (2007)
Manfred Einsiedler, Thomas Ward
Abstract. The exact order of mixing for zero-dimensional algebraic dynamical systems is not entirely understood. Here non-Archimedean norms in function fields of positive characteristic are used to...
London Mathematical Society ISSN 1461--1570 PRIMES IN ELLIPTIC DIVISIBILITY SEQUENCES (2007)
Morgan Ward pursued the study of elliptic divisibility sequences initiated by Lucas, and Chudnovsky and Chudnovsky suggested looking at elliptic divisibility sequences for prime appearance. The...
Manfred Einsiedler, For Algebraic
on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of R d. Here we completely describe this expansive behavior for the class of...
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...
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...
Ratner's theorem on SL(2,R)-invariant measures (2006)
We give a relatively short and self contained proof of Ratner's theorem in the special case of SL(2,R)-invariant measures.
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...
Measure rigidity and $p$-adic Littlewood-type problems (2005)
Einsiedler, Manfred, Kleinbock, Dmitry
The paper investigates various $p$-adic versions of Littlewood's conjecture, generalizing a set-up considered recently by de Mathan and Teulie. In many cases it is shown that the sets of exceptions...
Non-archimedean amoebas and tropical varieties (2004)
Einsiedler, Manfred, Kapranov, Mikhail, Lind, Douglas
We study the non-archimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For...
Non-archimedean amoebas and tropical varieties (2004)
Manfred Einsiedler, Mikhail Kapranov, Douglas Lind
Abstract. We study the non-archimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For...
Non-archimedean amoebas and tropical varieties (2004)
Manfred Einsiedler, Mikhail Kapranov, Douglas Lind
Abstract. We study the non-archimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For...
Isomorphism rigidity in entropy rank two (2003)
Einsiedler, Manfred, Ward, Thomas
We study the rigidity properties of a class of algebraic Z^3-actions with entropy rank two. For this class, conditions are found which force an invariant measure to be the Haar measure on an affine...
Periodic points for good reduction maps on curves (2003)
Einsiedler, Manfred, Everest, Graham, Ward, Thomas
The periodic points of a morphism of good reduction for a smooth projective curve with good reduction over the p-adics form a discrete set. This is used to give an interpretation of the morphic...
Entropy geometry and disjointness for zero-dimensional algebraic actions (2002)
Einsiedler, Manfred, Ward, Thomas
We show that many algebraic actions of higher-rank abelian groups on zero-dimensional groups are mutually disjoint. The proofs exploit differences in the entropy geometry arising from subdynamics and...
Asymptotic geometry of non-mixing sequences (2002)
Einsiedler, Manfred, Ward, Thomas
The exact order of mixing for zero-dimensional algebraic dynamical systems is not entirely understood. Here non-Archimedean norms in function fields of positive characteristic are used to exhibit an...
Morphic heights and periodic points (2002)
Einsiedler, Manfred, Everest, Graham, Ward, Thomas
An approach to the calculation of local canonical morphic heights is described, motivated by the analogy between the classical height in Diophantine geometry and entropy in algebraic dynamics. We...
Algebraic Z^d-Actions of Entropy Rank One (2002)
Manfred Einsiedler, Douglas Lind
We investigate algebraic Z -actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of...
Expansive subdynamics for algebraic $Z^d$-actions (2001)
Einsiedler, Manfred, Lind, Douglas, Miles, Richard, Ward, Thomas
A general framework for investigating topological actions of $Z^d$ on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of $R^d$....
ACTIONS OF ALGEBRAIC Z d-ACTIONS OF RANK ONE (2001)
The Erwin, Schrödinger International Boltzmanngasse, Manfred Einsiedler, Klaus Schmidt, Manfred Einsiedler, Klaus Schmidt
Abstract. In this paper we consider Z d-actions, d ≥ 1, by automorphisms of compact connected abelian groups which contain at least one expansive automorphism (such actions are called algebraic Z...
When does a Polynomial Ideal Contain a Positive Polynomial? (2000)
The Erwin, Schrodinger International Boltzmanngasse, Manfred Einsiedler, Manfred Einsiedler, Selim Tuncel, Selim Tuncel
. We use Grobner bases and a theorem of Handelman to show that an ideal I of R[x 1 ; : : : ; x k ] contains a polynomial with positive coecients if and only if no initial ideal in v (I), v 2 R k ,...
Expansive Subdynamics for Algebraic ...-Actions (2000)
The Erwin, Schrodinger International Boltzmanngasse, Manfred Einsiedler, Douglas Lind, Richard Miles, Richard Miles, ...
. A general framework for investigating topological actions of Z d on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower dimensional subspaces of R d ....