Related papers: Local Entropy Theory of a Random Dynamical System
In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…
We introduce local topological entropy $h_{\text{top}}(T, \mathcal{U})$ and two kinds of local measure-theoretic entropy $h_{\mu}^{(r)-}(T,\mathcal{U})$ and $h_{\mu}^{(r)+}(T,\mathcal{U})$ for random bundle transformations. We derive a…
In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and…
For random dynamical systems, by summarizing the fundamental properties of Kifer's topological pressure we introduce the concept of random pressure functions, and define Ruelle's metric entropy for invariant measures. Employing the…
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…
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic…
This paper is a survey about recent developments in the local entropy theory for topological dynamical systems and continuous group actions, with particular emphasis on the connections with other areas of dynamical systems and mathematics.
The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in…
This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective…
In this paper, we investigate induced and nonlinear fiber topological pressure for random dynamical systems. We define a non-averaged induced fiber pressure via spanning and separated sets, characterize it as the pseudo-inverse of the…
In this paper, we define the topological pressure for sub-additive potentials via separated sets in random dynamical systems and we give a proof of the relativized variational principle for the topological pressure.
Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as a counterpart of Bowen topological entropy. In the present paper, we will give a systematically study to the packing topological entropy for…
A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it…
We introduce the relative tail entropy to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail entropy is conserved by the principal extension.
This paper discusses the variational principles on subsets for topological pressure and topological entropy of non-autonomous dynamical systems. We define the Pesin-Pitskel topological pressure (weighted topological pressure) and the Bowen…
The pre-image topological pressure is defined for bundle random dynamical systems. A variational principle for it has also been given.
Let $f_{i},i=1,2$ be continuous bundle random dynamical systems over an ergodic compact metric system $(\Omega,\mathcal{F},\mathbb{P},\vartheta)$. Assume that ${\bf a}=(a_{1},a_{2})\in\mathbb{R}^{2}$ with $a_{1}>0$ and $a_{2}\geq0$, $f_{2}$…
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…
For a given topological dynamical system $(X,T)$ over a compact set $X$ with a metric $d$, the "variational principle" states that \begin{equation*} \sup_{\mu}h_\mu(T) = h(T) = h_d(T), \end{equation*} where $h_\mu(T)$ is the…