A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any subset of the phase space eventually revisit the set. More precise information is provided by various ergodic theorems which assert that, under certain conditions, th...

1. Introduction. In this paper we announce the introduction of a new notion of amenability for ergodic group actions and ergodic equivalence relations. Amenable ergodic actions occupy a position in ergodic theory parallel to that of amenable groups in group theory and one can therefore expect this notion to be useful in diverse circumstances. Here we announce applications to hyperfinite factor ...

We prove that ergodicity of the horocycle ow on a surface of constant negative curvature is equivalent to ergodicity of the associated boundary action. As a corollary we obtain ergodicity of the horocycle ow on several large classes of covering surfaces. There are two natural \geometric ows" on (the unitary tangent bundle of) an arbitrary surface of constant negative curvature: the geodesic and...

We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these. §0 Introduction Let (X,B,m, T ) be an invertible, ergodic measure preserving transformation of a σ-finite measure space, then there are no other σ-finite, m-abso...

Γ-convergence methods are used to prove homogenization results for fractional obstacle problems in periodically perforated domains. The obstacles have random sizes and shapes and their capacity scales according to a stationary ergodic process. We use a trace-like representation of fractional Sobolev norms in terms of weighted Sobolev energies established in [8], a weighted ergodic theorem and a...

We consider discrete random magnetic Laplacians in the plane and discrete random electromagnetic Laplacians in higher dimensions. The existence of these objects relies on a theorem of Feldman-Moore which was generalized by Lind to the nonabelian case. For example, it allows to realize ergodic Schrr odinger operators with stationary independent magnetic elds on discrete two dimensional lattices ...

This paper is concerned with the approximation of the effective conductivity σ(A) associated to an elliptic operator ∇xA(x, η)∇x where for x ∈ R d, d ≥ 1, A(x, η) is a bounded elliptic random symmetric d × d matrix and η takes value in an ergodic probability space. Writing AN (x, η) the periodization of A(x, η) on the torus T d N of dimension d and side N we prove that η-a.s. lim N→+∞ σ(A (x, η...

Modeling the traffic flow at signalized intersections has been discussed in many works [1][2][3][4]. Though streets and intersections and designed to be Ergodic, the traffic flow during busy hours is not necessarily Ergodic. In this paper, we modeled the traffic at intersection during busy hours by using M/G/1 model. And based on the collected data, we modeled a special service distribution pat...

We give sufficient conditions for a shift space (Σ, σ) to be intrinsically ergodic, along with sufficient conditions for every subshift factor of Σ to be intrinsically ergodic. As an application, we show that every subshift factor of a β-shift is intrinsically ergodic, which answers an open question included in Mike Boyle’s article “Open problems in symbolic dynamics”. We obtain the same result...

We study quasiperiodically forced circle homeomorphisms and derive a basic classification with respect to the invariant ergodic measures for such systems: Either there exists an invariant graph and every invariant ergodic measure is associated to some invariant graph, or the system is uniquely ergodic. This immediately verifies an observation which is well-known from numerical studies, namely t...