<p style='text-indent:20px;'>The classical theorem of Jewett and Krieger gives a strictly ergodic model for any measure preserving system. An extension this result non-ergodic systems was given many years ago by George Hansel. He constructed, system, uniform model, i.e. compact space which admits an upper semicontinuous decomposition into models the components measure. In note we give new...

We prove an L subsequence ergodic theorem for sequences chosen by independent random selector variables, thereby showing the existence of sparser universally L-good sequences than had been previously established. We extend this theorem to a more general setting of ergodic group actions.

Abstract. In this article we establish a substitution theorem for semilinear stochastic evolution equations (see’s) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techni...

An entangled ergodic theorem was introduced in [1] in connection with the quantum central limit theorem, and clearly formulated in [6]. Namely, let U be a unitary operator on the Hilbert space H, and for m ≥ k, α : {1, . . . , m} 7→ {1, . . . , k} a partition of the set {1, . . . , m} in k parts. The entangled ergodic theorem concerns the convergence in the strong, or merely weak (s–limit, or w...

We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem. Let (X,B, μ) be a probability space, T : X → X a (possibly noninvertible) measurepreserving transformation, and f ∈ L(X,B, μ). Let

This is an earlier, but more general, version of ”An L Ergodic Theorem for Sparse Random Subsequences”. We prove an L ergodic theorem for averages defined by independent random selector variables, in a setting of general measure-preserving group actions. A far more readable version of this paper is in the works.

By exploiting the Denjoy theorem in topological dynamics and the unique ergodic theorem in ergodic theory, we will give a classification of all solutions of asymmetric p-Laplacian oscillators with periodic coefficients. AMS (MOS) Subject Classification. Primary: 34D08; Secondary: 37E10, 37A25.

We offer a proof of the following nonconventional ergodic theorem: Theorem. If Ti : Z y (X,Σ, μ) for i = 1, 2, . . . , d are commuting probability-preserving Z-actions, (IN )N≥1 is a Følner sequence of subsets of Z, (aN )N≥1 is a base-point sequence in Z and f1, f2, . . . , fd ∈ L∞(μ) then the nonconventional ergodic averages