Related papers: Nonsingular transformations that are ergodic with …
Downarowicz and Maass (2008) proposed topological ranks for all homeomorphic Cantor minimal dynamical systems using properly ordered Bratteli diagrams. In this study, we adopt this definition to the case of all essentially minimal…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological…
We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…
We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then provide a result linking the ergodic optimizations of elements of a C*-dynamical system to the convergence of…
We consider dynamical systems generated by partially hyperbolic surface endomorphisms of class C^r with one-dimensional strongly unstable subbundle. As the main result, we prove that such a dynamical system generically admits finitely many…
We consider a nonstationary sequence of independent random isometries of a compact metrizable space. Assuming that there are no proper closed subsets with deterministic image we establish a weak-* convergence to the unique invariant under…
We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along…
The main result of this note, Theorem 2, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant under the action of the infinite unitary group and that admits well-defined projections onto the…
We prove a model theorem for factor maps between ergodic, infinite measure-preserving systems.
Monomial mappings, $x\mapsto x^n$, are topologically transitive and ergodic with respect to Haar measure on the unit circle in the complex plane. In this paper we obtain an anologous result for monomial dynamical systems over $p-$adic…
Let $M=X/\Gamma$ be a geometrically finite negatively curved manifold with fundamental group $\Gamma$ acting on $X$ by isometries. The purpose of this paper is to study the mixing property of the geodesic flow on $T^1M$, the asymptotic…
We prove the existence of an ergodic measure with full Hausdorff dimension for a class of nonlinear nonconformal skew-product transformations. In order to do so we establish a variational principle for the topological pressure of certain…
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 introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $E\subset\Bbb N\cup\{\infty\}$ as the set of essential…
Invariant ergodic measures for generalized Boole type transformations are studied using an invariant quasi-measure generating function approach based on special solutions to the Frobenius--Perron operator. New two-dimensional Boole type…
We show that the the shift on the reduced C*--algebras of RD--groups, including the free group on infinitely many generators, and the amalgamated free product C*--algebras, enjoys the very strong ergodic property of the convergence to the…
We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…
Let S be an ergodic measure-preserving automorphism on a non-atomic probability space, and let T be the time-one map of a topologically weak mixing suspension flow over an irreducible subshift of finite type under a Holder ceiling function.…
We discuss an invertible version of Furstenberg's `Ergodic CP Shift Systems'. We show that the explicit regularity of these dynamical systems with respect to magnification of measures, implies certain regularity with respect to translation…