Related papers: Ergodic Theory: Recurrence

We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions…

In this expository paper, we survey nowadays classical tools or criteria used in problems of convergence everywhere to build counterexamples: the Stein continuity principle, Bourgain's entropy criteria and Kakutani-Rochlin lemma, most…

We prove second and fourth order improved Poincar\'e type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as…

We introduce the concepts of Baire Ergodicity and Ergodic Formalism, employing them to study topological and statistical attractors. Specifically, we establish the existence and finiteness of such attractors and provide applications for…

We explicitly derive, following a Noether-like approach, the criteria for preserving Poincare invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that,…

Physical nature of widely known Ramsey fringes phenomenon is discussed.

We study the return probability for the Anderson model on the random regular graph and give evidence of the existence of two distinct phases: a fully ergodic and nonergodic one. In the ergodic phase, the return probability decays…

In this article, intended for the Handbook of Recursion Theory, we survey recursion theory on the ordinal numbers, with sections devoted to $\alpha$-recursion theory, $\beta$-recursion theory and the study of the admissibility spectrum.

We study various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of weighted means. Our main…

Gauge theories of gravity provide an elegant and promising extension of general relativity. In this paper we show that the Poincar\'e gauge theory exhibits gravity-induced birefringence under the assumption of a specific gauge invariant…

For random dynamical systems, by summarizing the fundamental properties of Kifer's topological pressure we introduce the concept of random pressure functions, and define Ruelle's metric entropy for invariant measures. Employing the…

Some principal problems of general relativity theory and attempts of their solution are discussed. The Poincare gauge theory of gravity as natural generalization of Einsteinian gravitation theory is considered. The changes of gravitational…

Many integrable physical systems exhibit Keplerian shear. We look at this phenomenon from the point of view of ergodic theory, where it can be seen as mixing conditionally to an invariant $\sigma$-algebra. In this context, we give a…

A three term recurrence relation is derived for a basis consisting of polynomials multiplied by sines and cosines with large, but fixed frequencies. A numerical method for computing the coefficients of the three term recurrence relation is…

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…

Infinite order linear recurrences are studied via kneading matrices and kneading determinants. The concepts of kneading matrix and kneading determinant of an infinite order linear recurrence, introduced in this work, are defined in a purely…

We describe a framework for a generalized nonlocal gravity theory inspired by Poincar\'e gauge theory. Our theory provides a unified description of previous nonlocal extensions of Einstein's theory of gravitation, in particular it allows…

Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighborhood of the origin. We address this question in…

We consider several fundamental properties of grand variable exponent Lebesgue spaces. Moreover, we discuss Ergodic theorems in these spaces whenever the exponent is invariant under the transformation.