Related papers: On the multiple recurrence properties for disjoint…

We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting $\mathbb{R}$-actions, coming from a single jointly measurable measure-preserving $\mathbb{R}^2$-action on a probability space. The key ingredient…

We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one based on functional inequalities (of…

Let $T:[0,1]^d \rightarrow[0,1]^d$ be a piecewise expanding map with an absolutely continuous (with respect to the $d$-dimensional Lebesgue measure $m_d$) $T$-invariant probability measure $\mu$. Let $\left\{\mathbf{r}_n\right\}$ be a…

We study invariant ergodic measures for quasiperiodically forced circle homeomorphisms and derive that either the system is uniquely ergodic or any such measure is associated to some invariant multigraph.

We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khintchine's recurrence theorem obtained by Bergelson in the measure theoretic case. A noncommutative…

In the paper we consider $T_{1},..., T_{d}$ absolute contractions of von Neumann algebra $\M$ with normal, semi-finite, faithful trace, and prove that for every bounded Besicovitch weight $\{a(\kb)\}_{\kb\in\bn^d}$ and every $x\in…

We study a class of homeomorphisms of surfaces collectively known as linked-twist maps. We introduce an abstract definition which enables us to give a precise characterisation of a property observed by other authors, namely that such maps…

We consider an intermediate factor situation in two categories: probability measure preserving ergodic theory and compact topological dynamics. In the first we prove a master-key theorem and examine a wide range of applications. In the…

It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p-$space, $1\leq p<\infty$ or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge…

Let $S$ and $T$ be measure-preserving transformations of a probability space $(X,{\mathcal B},\mu)$. Let $f$ be a bounded measurable functions, and consider the integrals of the corresponding `double' ergodic averages:…

For a system of two measures supported on a starlike set in the complex plane, we study asymptotic properties of associated multiple orthogonal polynomials $Q_{n}$ and their recurrence coefficients. These measures are assumed to form a…

We survey some recent developments and give a list of open problems regarding multiple recurrence and convergence phenomena of $\mathbb{Z}^d$ actions in ergodic theory and related applications in combinatorics and number theory.

We compare self-joining- and embeddability properties. In particular, we prove that a measure preserving flow $(T_t)_{t\in\mathbb{R}}$ with $T_1$ ergodic is 2-fold quasi-simple (2-fold distally simple) if and only if $T_1$ is 2-fold…

We develop a robust structure theory for multiple ergodic averages of commuting transformations along Hardy sequences of polynomial growth. We then apply it to derive a number of novel results on joint ergodicity, recurrence and…

We prove that multiple-recurrence and polynomial-recurrence of invertible infinite measure preserving transformations are both properties which pass to extensions.

Let $(X,\mathcal{A}, \mu)$ be a probability measure space and let $T_i,$ $1\leq i\leq H,$ be invertible bi measurable measure preserving transformations on this measure space. We give a sufficient condition for the product of $H$ bounded…

We study multiple recurrence properties along separated cross sections for pmp actions of unimodular lcsc group on Polish spaces. We establish a multiple transverse recurrence theorem under the assumption that sufficiently large powers of…

We study a compactification of the space of invariant probability measures for a transitive countable Markov shift. We prove that it is affine homeomorphic to the Poulsen simplex. Furthermore, we establish that, depending on a combinatorial…

We introduce a new class of sparse sequences that are ergodic and pointwise universally $L^2$-good for ergodic averages. That is, sequences along which the ergodic averages converge almost surely to the projection to invariant functions.…

For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…