Related papers: On Ergodic Hypothesis

The HRT conjecture states that any finite collection of time-frequency shifts of a non-zero square-integrable function on the real line is linearly independent. In this paper, we establish the linear independence of finite systems of…

Recently O. Sarig has introduced and explored the concept of positively recurrent functions. In this paper we construct a natural wide class of such functions and we showthat they have stronger ergodic properties than the general functions…

We prove a Universal Coefficient Theorem for objects in the bootstrap class in the equivariant Kasparov category for a finite cyclic group of square-free order.

In this paper we study the ergodic theory and thermodynamic formalism of the geodesic flow on non-compact pinched negatively curved manifolds. We consider two notions of entropy at infinity, the topological and the measure theoretic entropy…

We show that the ergodicity of an aperiodic automorphism of a Lebesgue space is equivalent to the continuity of a certain map on a metric Boolean algebra. A related characterization is also presented for periodic and totally ergodic…

We prove a model theorem for factor maps between ergodic, infinite measure-preserving systems.

We show that ``ergodic regime'' appears for generic dispersion relations in the semiclassical motion of electrons in a metal and we prove that, in the fixed energy picture, the measure of the set of such directions is zero.

For stochastic $C_0$-semigroups on $L^1$-spaces there is wealth of results that show strong convergence to an equilibrium as $t \to \infty$, given that the semigroup contains a partial integral operator. This has plenty of applications to…

A unified view is given to recent developments about a systematic method of constructing rational mappings as ergodic transformations with non-uniform invariant measures on the unit interval I=[0,1]. All of the rational ergodic mappings of…

We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ in the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. In the case $\nu=2$ we prove (the full hyperbolicity and) the ergodicity of such…

We prove almost sure ergodic theorems for a class of systems called quasistatic dynamical systems. These results are needed, because the usual theorem due to Birkhoff does not apply in the absence of invariant measures. We also introduce…

An algebraic $\Gamma$-action is an action of a countable group $\Gamma$ on a compact abelian group $X$ by continuous automorphisms of $X$. We prove that any expansive algebraic action of a finitely generated nilpotent group $\Gamma$ on a…

We prove pointwise and maximal ergodic theorems for probability measure preserving (p.m.p.) actions of any countable group, provided it admits an essentially free, weakly mixing amenable action of stable type $III_1$. We show that this…

We present a new approach to the proof of ergodic theorems for actions of free groups based on geometric covering and asymptotic invariance arguments. Our approach can be viewed as a direct generalization of the classical geometric covering…

We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full…

In this article we give evaluations of certain series of hyperbolic functions, using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.

In this paper we introduce a property of ergodic flows, called Property B. We prove that any ergodic hyperfinite equiva- lence relation of type III_o whose associated flow satisfies this property is not of product type. A consequence of…

We show that for odd-valued piecewise-constant skew products over a certain two parameter family of interval exchanges, the skew product is ergodic for a full-measure choice of parameters.

We obtain a partial converse of Vershik's description of ergodic probability measures on a compact metric space with respect to an isometric action by an inductively compact group. This allows us to identify, in this setting, the set of…

Under the assumption of a natural subadditive potential, the so called cylinder function, working on the symbol space we prove the existence of the ergodic invariant probability measure satisfying the equilibrium state. As an application we…