Related papers: What does a rate in a mean ergodic theorem imply?

This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…

We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting…

In this review we survey the literature on mean-field coupled maps. We start with the early works from the physics literature, arriving to some recent results from ergodic theory studying the thermodynamic limit of globally coupled maps and…

We initiate the study of effective pointwise ergodic theorems in resource-bounded settings. Classically, the convergence of the ergodic averages for integrable functions can be arbitrarily slow. In contrast, we show that for a class of…

Inspired by topological Wiener-Wintner theorems we study the mean ergodicity of amenable semigroups of Markov operators on $C(K)$ and show the connection to the convergence of strong and weak ergodic nets. The results are then used to…

In this paper we are concerned with the study of additive ergodic averages in multiplicative systems and the investigation of the "pretentious" dynamical behaviour of these systems. We prove a mean ergodic theorem (Theorem A) that…

We establish an Ergodic Theorem for lower probabilities, a generalization of standard probabilities widely used in applications. As a by-product, we provide a version for lower probabilities of the Strong Law of Large Numbers.

We give a simple construction involving partial actions which permits us to obtain an easy proof of a weakened version of L. O'Carroll's theorem on idempotent pure extensions of inverse semigroups.

A mid-point theorem is proved in an elementary way for the U type shape of functions that arise out of exponential quadratic functions. These results are inspired from epidemic patterns and growth over a time period. Key words: natural…

We generalize the constructions of [17,19] to layered semirings, in order to enrich the structure and provide finite examples for applications in arithmetic (including finite examples). The layered category theory of [19] is extended…

In the present paper, we consider random invariant densities and the mean ergodic theorem for Markov operator cocycles which are applicable to quenched type random dynamical systems. We give necessary and sufficient conditions for the…

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropies

We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…

Dynamical systems that are contracting on a subspace are said to be semicontracting. Semicontraction theory is a useful tool in the study of consensus algorithms and dynamical flow systems such as Markov chains. To develop a comprehensive…

A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of…

A general or truss distributive laws between two associative operations on the same set are studied for cancellative and inverse semigroups.

In this paper, we extend recent results on the convergence of ergodic averages along sequences generated by return times to shrinking targets in rapidly mixing systems, partially answering questions posed by the first author, Maass and the…

We prove mean and pointwise ergodic theorems for the action of a discrete lattice subgroup in a connected algebraic Lie group, on infinite volume homogeneous algebraic varieties. Under suitable necessary conditions, our results are…

We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages of sequences with terms in a given finite set A. For every such set we completely characterize the numbers x ("intermediate values") with…

This article is devoted to studying individual ergodic theorems for subsequential weighted ergodic averages on the noncommutative Lp-spaces associated to a semifinite von Neumann algebra M. In particular, we establish the convergence of…