Related papers: Properly ergodic structures

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…

We show that given any subgroup F of R_+ which is either countable or belongs to a certain "large" class of uncountable subgroups, there exist continuously many free ergodic probability measure preserving actions \sigma_i of the free group…

We provide sufficient conditions for the existence of a trace on the essential $\mathrm{C}^\ast$-algebra of a (not necessarily Hausdorff) \'etale groupoid $G$ which extends an invariant measure $\mu$ on the unit space of $G$. In particular,…

We study the topology of the space of probability measures invariant under the geodesic flow, defined on the unit-tangent bundle of a compact Riemannian manifold with non-positive curvature. Building on a previous work by Coud\`ene and…

We prove that a shift ergodic measure on a topologically mixing sub-shift is isomorphic to a Bernoulli shift whenever it is quasi invariant under permutations of finite number of coordinates. We prove also that Gibbs measures on…

A reduction of properties (invariants) of compact sets of real numbers to properties of countable orders is presented here. Discussed here is also an embedding property of some compact sets that are called t$\mathbb R$-sets. Among others,…

It is known that for every second countable locally compact group G, there exists a proper G-invariant metric which induces the topology of the group. This is no longer true for coset spaces G/H viewed as G-spaces. We study necessary and…

Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This…

We give a sufficient condition for the ergodicity of the Lebesgue measure for an iterated function system of diffeomorphisms. This is done via the induced iterated function system on the space of continuum (which is called hyper-space). We…

We state and prove a generalization of Kingman's ergodic theorem on a measure-preserving dynamical system $(X,\mathcal{F},\mu,T)$ where the $\mu$-almost sure subadditivity condition $f_{n+m} \leq f_n + f_m \circ T^{n}$ is relaxed to a…

We introduce the concept of a heterodimensional cycle of hyperbolic ergodic measures and a special type of them that we call rich. Within a partially hyperbolic context, we prove that if two measures are related by a rich heterodimensional…

The classical Birkhoff ergodic theorem in its most popular version says that the time average along a single typical trajectory of a dynamical system is equal to the space average with respect to the ergodic invariant distribution. This…

We introduce an ergodic approach to the study of {\em joint normality} of representations of numbers. For example, we show that for any integer $b \geq 2$ almost every number $x \in [0,1)$ is jointly normal with respect to the $b$-expansion…

In this article we give a classification of the binary, simple, $\omega$-categorical structures with SU-rank 1 and trivial pregeometry. This is done both by showing that they satisfy certain extension properties, but also by noting that…

Let $X$ be a compact complex surface. Consider a finitely supported probability measure $\mu$ on $\text{Aut}(X)$ such that $\Gamma_{\mu} = \langle \text{Supp}(\mu)\rangle<\text{Aut}(X)$ is non-elementary. We do not assume that…

We consider the problem of ergodicity for the $P(\Phi)_2$ measure of quantum field theory under the flow of the singular stochastic (damped) wave equation $u_{tt} + u_t + (1-\Delta) u + {:}\,p(u)\mspace{2mu}{:} = \sqrt 2 \xi$, posed on the…

We show that the $\mathscr{B}$-free subshift $(S,X_{\mathscr{B}})$ associated to a $\mathscr{B}$-free system is intrinsically ergodic, i.e.\ it has exactly one measure of maximal entropy. Moreover, we study invariant measures for such…

We show that for any C^1+alpha diffeomorphism of a compact Riemannian manifold, every non-atomic, ergodic, invariant probability measure with non-zero Lyapunov exponents is approximated by uniformly hyperbolic sets in the sense that there…

We study the first-order almost-sure theories for classes of finite structures that are specified by homomorphically forbidding a set $\mathcal{F}$ of finite structures. If $\mathcal{F}$ consists of undirected graphs, a full description of…

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…