Related papers: The variational principle of topological pressure …

This study establishes the variational principle for local pressure in the sofic context.

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, 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 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 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.

This paper aims to investigate the thermodynamic formalism of weighted amenable topological pressure for factor maps of amenable group actions. Following the approach of Tsukamoto [\emph{Ergodic Theory Dynam. Syst.} \textbf{43}(2023),…

The notion of topological pressure was introduced by Ruell and also he formulated a variational principle for the topological pressure. Pesin and Pitskel introduced a definition of topological on subsets inspired by Hausdorff dimension. In…

We introduce four, a priori different, notions of topological pressure for possibly discontinuous semiflows acting on compact metric spaces and observe that they all agree with the classical one when restricted to the continuous setting.…

The pre-image topological pressure is defined for bundle random dynamical systems. A variational principle for it has also been given.

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.

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…

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…

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…

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…

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.

In this paper, we first prove the variational principle for amenable packing topological pressure. Then we obtain an inequality concerning amenable packing pressure for factor maps. Finally, we show that the equality about packing…

Let $r\geq 2$ and $(X_i,G)$ $(i=1,\cdots,r)$ be topological dynamical systems with $G$ being an infinite discrete amenable group. Suppose that $\pi_i:(X_i,G)\to (X_{i+1},G)$ are factor maps and $0\leq w_i\leq 1$. In this article, for $f\in…

This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational…

In this paper we state the variational principle for the weighted porous media equation. It extends V.I. Arnold's approach to the description of Euler flows as a geodesics on some manifold, i.e. as a critical points of some energy…

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…