Related papers: On invariant measures for $\mathscr{B}$-free syste…

We study the finiteness of physical measures for skew-product transformations $F$ associated with discrete-time random dynamical systems driven by ergodic Markov chains. We develop a framework, using an independent and identically…

For every positive integer $n\geq 2$, we introduce the concept of measure-theoretic $n$-sensitivity for measure-theoretic dynamical systems via finite measurable partitions, and show that an ergodic system is measure-theoretically…

We consider skew-products with concave interval fiber maps over a certain subshift obtained as the projection of orbits staying in a given region. It generates a new type of (essentially) coded shift. The fiber maps have expanding and…

In 2010, Bezuglyi, Kwiatkowski, Medynets and Solomyak [Ergodic Theory Dynam. Systems 30 (2010), no.4, 973-1007] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard…

This paper studies ergodic properties of certain measures arising in the dynamics of holomorphic correspondences. These measures, in general, are not invariant in the classical sense of ergodic theory. We define a notion of ergodicity, and…

We give sufficient conditions for intervals $(a,b)$ such that the associated open dynamical system for the doubling map is intrinsically ergodic. We also show that the set of parameters $(a,b) \in (\frac{1}{4}, \frac{1}{2}) \times…

Given a finite-to-one factor code $\pi: X \to Y$ between irreducible sofic shifts and an ergodic $\nu$ on $Y$ with full support, it is known that the fiber $\pi^{-1}_*(\nu)$ has at most $d_\pi$ ergodic measures in it where $d_\pi$ is the…

We consider a conservative ergodic measure-preserving transformation $T$ of a $\sigma$-finite measure space $(X,\mathcal{B},\mu)$ with $\mu(X)=\infty$. Given an observable $f:X\to \mathbb{R}$ we study the almost sure asymptotic behaviour of…

We define a general notion of a smooth invariant (central) ergodic measure on the space of paths of an $N$-graded graph (Bratteli diagram). It is based on the notion of standardness of the tail filtration in the space of paths, and the…

We study transitive step skew-product maps modeled over a complete shift of $k$, $k\ge2$, symbols whose fiber maps are defined on the circle and have intermingled contracting and expanding regions. These dynamics are genuinely nonhyperbolic…

Let $H$ be the space of all Hermitian matrices of infinite order and $U(\infty)$ be the inductive limit of the chain $U(1)\subset U(2)\subset...$ of compact unitary groups. The group $U(\infty)$ operates on the space $H$ by conjugations,…

Given a finite-to-one factor map $\pi: (X, T) \to (Y, S)$ between topological dynamical systems, we look into the pushforward map $\pi_*: M(X, T) \to M(Y,T)$ between sets of invariant measures. We investigate the structure of the measure…

We show that a modification of the proof of our paper [CvELNR18], in the spirit of [FP81], shows delocalisation in the long-range Discrete Gaussian Chain, and generalisations thereof, for any decay power $\alpha>2$ and at all temperatures.…

We show that some $C^*$--dynamical systems obtained by "quantizing" classical ones on the free Fock space, enjoy very strong ergodic properties. Namely, if the classical dynamical system $(X, T, \m)$ is ergodic but not weakly mixing, then…

We show evidence, based on extensive and carefully performed numerical experiments, that the system of two elastic hard-point masses in one-dimension is not ergodic for a generic mass ratio and consequently does not follow the principle of…

Given a factor code $\pi$ from a one-dimensional shift of finite type $X$ onto an irreducible sofic shift $Y$, if $\pi$ is finite-to-one there is an invariant called the degree of $\pi$ which is defined the number of preimages of a typical…

We study ergodic-theoretic properties of coded shift spaces. A coded shift space is defined as a closure of all bi-infinite concatenations of words from a fixed countable generating set. We derive sufficient conditions for the uniqueness of…

For any $n\geq 3$, let $1<\beta<2$ be the largest positive real number satisfying the equation $$\beta^n=\beta^{n-2}+\beta^{n-3}+\cdots+\beta+1.$$ In this paper we define the shrinking random $\beta$-transformation $K$ and investigate…

In this paper, we explore a topological system $f:M\rightarrow M$ with average shadowing property. We extend Sigmund's results and show that every non-empty, compact and connected subset $V\subseteq\mathcal {M}_{inv}(f)$ coincides with…

In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to…