相关论文: On the interplay between measurable and topologica…
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…
We survey the connections between entropy, chaos, and independence in topological dynamics. We present extensions of two classical results placing the following notions in the context of symbolic dynamics: 1. Equivalence of positive entropy…
We answer positively a question of Ryzhikov, namely we show that being a relatively weakly mixing extension is a comeager property in the Polish group of measure preserving transformations. We study some related classes of ergodic…
For a locally compact sofic group continuously acting on a compact metric space, we first study the relative sofic entropy and prove an additive inequality relating sofic entropy and relative sofic entropy. Moreover, it is shown that the…
We show that a non-wandering dynamical system with the shadowing property is either equicontinuous or has positive entropy and that in this context uniformly positive entropy is equivalent to weak mixing. We also show that weak mixing…
In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…
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…
This tutorial gives an overview of some of the basic techniques of measure theory. It includes a study of Borel sets and their generators for Polish and for analytic spaces, the weak topology on the space of all finite positive measures…
For random compositions of independent and identically distributed measurable maps on a Polish space, we study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical…
We study properties of some popular topology on the space of Borel probabilities on a topological ambient space in this paper. We show that the two types of popular vague topology are equivalent to each other in case the ambient space is…
Let $G$ be a countably infinite group, and let $\mu$ be a generating probability measure on $G$. We study the space of $\mu$-stationary Borel probability measures on a topological $G$ space, and in particular on $Z^G$, where $Z$ is any…
The dissertation describes ergodic properties of some stochastic dynamical systems generated by Markov chains with values in the state space which is a Polish space. The mathematical model describing the process of cell division is…
Let $(X,d,f)$ be a topological dynamical system, where $(X,d)$ is a compact metric space and $f:X\to X$ is a continuous map. We define $n$-ordered empirical measure of $x\in X$ by \begin{align*}…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
In this paper, we introduce topological pressure for continuous actions of countable sofic groups on compact metrizable spaces. This generalizes the classical topological pressure for continuous actions of countable amenable groups on such…
In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and…
In the variational approach to statistical mechanics, equilibrium states are the rigorous analogues of thermodynamic phases; the question of which invariant measures can arise as equilibrium states is therefore the question of which phases…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
We introduce a functor which associates to every measure preserving system (X,B,\mu,T) a topological system (C_2(\mu),\tilde{T}) defined on the space of 2-fold couplings of \mu, called the topological lens of T. We show that often the…
We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…