Related papers: M\"obius disjointness along ergodic sequences for …

Let $T$ be an $\R$-tree in the boundary of Outer space with dense orbits. When the free group $\FN$ acts freely on $T$, we prove that the number of projective classes of ergodic currents dual to $T$ is bounded above by $3N-5$. We combine…

For Axiom A diffeomorphisms and flows, the celebrated Spectral Decomposition Theorem of Smale states that the non-wandering set decomposes into a finite disjoint union of isolated compact invariant sets, each of which is the homoclinic…

This paper is aim to extend Kenneth R. Berg's findings on the maximal entropy theorem and the ergodicity of measure convolution to the case of surjective homomorphisms. We further explores dynamical systems under surjective homomorphism in…

In this paper, we conduct a comprehensive study on ergodic properties of the geodesic flow on a $C^\infty$ uniform visibility manifold $M$ without conjugate points. If $M$ is a closed surface of genus at least two without conjugate points,…

A dynamical Mertens' theorem for ergodic toral automorphisms with error term O(N^{-1}) is found, and the influence of resonances among the eigenvalues of unit modulus is examined. Examples are found with many more, and with many fewer,…

In 2010, Sarnak initiated the study of the dynamics of the system determined by the square of the M\"obius function (the characteristic function of the square-free integers). We deal with his program in the more general context of…

Extending a result by Chilin and Litvinov, we show by construction that given any $\sigma$-finite infinite measure space $(\Omega,\mathcal{A}, \mu)$ and a function $f\in L^1(\Omega)+L^\infty(\Omega)$ with $\mu(\{|f|>\varepsilon\})=\infty$…

We study the problem on the weak-star decomposability of a topological $\mathbb{N}_{0}$-dynamical system $(\Omega,\varphi)$, where $\varphi$ is an endomorphism of a metric compact set $\Omega$, into ergodic components in terms of the…

In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…

Let $\mathbb F=\mathbb R$ or $\mathbb C$ and $n\in\b N$. Let $(S_k)_{k\ge0}$ be a time-homogeneous random walk on $GL_n(\b F)$ associated with an $U_n(\b F)$-biinvariant measure $\nu\in M^1(GL_n(\b F))$. We derive a central limit theorem…

For each \beta\in(0,+\infty) there exists a canonical measure \mu_\beta on the ring A_f of finite adeles. We show that the positive rationals act ergodically on (A_f,\mu_\beta) for \beta\in(0,1], and then deduce from this the uniqueness of…

Consider a Markov process $\{\Phi(t) : t\geq 0\}$ evolving on a Polish space ${\sf X}$. A version of the $f$-Norm Ergodic Theorem is obtained: Suppose that the process is $\psi$-irreducible and aperiodic. For a given function $f\colon{\sf…

Local mean and individual (with respect to almost uniform convergence in Egorov's sense) ergodic theorems are established for actions of the semigroup $\mathbb R_+^d$ in symmetric spaces of measurable operators associated with a semifinite…

We study random perturbations of multidimensional piecewise expanding maps. We characterize absolutely continuous stationary measures (acsm) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of…

Using tools from the theory of optimal transport, we establish several results concerning isometric actions of amenable topological groups with potentially unbounded orbits. Specifically, suppose $d$ is a compatible left-invariant metric on…

We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full…

We establish characterization results for the ergodicity of stationary symmetric $\alpha$-stable (S$\alpha$S) and $\alpha$-Frechet random fields. We show that the result of Samorodnitsky [Ann. Probab. 33 (2005) 1782-1803] remains valid in…

The following question due to Thouvenot is well-known in ergodic theory. Let $S$ and $T$ be automorphisms of a probability space and let $ S \otimes S $ be isomorphic to $T \otimes T $. Could $S$ be not isomorphic to $T$? Our note contains…

We establish a connection between the structure of a stationary symmetric alpha-stable random field (0 < alpha < 2) and ergodic theory of non-singular group actions, elaborating on a previous work by Rosinski (2000). With the help of this…

We study the ergodic properties of generic continuous dynamical systems on compact manifolds. As a main result we prove that generic homeomorphisms have convergent Birkhoff averages under continuous observables at Lebesgue almost every…