Related papers: Pre-image Variational Principle for Bundle Random …

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…

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.

In this paper, inspired by the article [5], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure.

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…

In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…

This article establishes the variational principle of topological pressure for actions of sofic groupoids.

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…

We define the topological pressure for any sub-additive potentials of the countable discrete amenable group action and any given open cover. A local variational principle for the topological pressure is established.

We investigate the relationship between various topological pressures and the corresponding measure-theoretic pressures for nonautonomous dynamical systems based on the Carath\'eodory-Pesin structure. We prove a pressure distribution…

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 introduce a concept of nonlinear local topological pressure defined via open covers and establish a corresponding variational principle. Furthermore, we provide multiple equivalent characterizations of nonlinear pressure…

Let $\pi:X\to Y$ be a factor map, where $(X,T)$ and $(Y,S)$ are topological dynamical systems. Let ${\bf a}=(a_1,a_2)\in {\Bbb R}^2$ with $a_1>0$ and $a_2\geq 0$, and $f\in C(X)$. The ${\bf a}$-weighted topological pressure of $f$, denoted…

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…

We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…

We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.

This paper is devoted to the study of induced topological pressure, including both classical and nonlinear cases. For the classical induced topological pressure, we investigate equilibrium states, subdifferential and freezing states, while…

The goal of this paper is to define and investigate those topological pressures, which is an extension of topological entropy presented by Feng and Huang [13], of continuous transformations. This study reveals the similarity between many…

Topological pressures of the preimages of $\epsilon$-stable sets and some certain closed subsets of stable sets in positive entropy systems are investigated. It is showed that the topological pressure of any topological system can be…

Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical…