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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…

Dynamical Systems · Mathematics 2024-12-24 Chang-Bing Li

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.

Dynamical Systems · Mathematics 2015-06-23 Zhitao Xing , Ercai Chen

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…

Dynamical Systems · Mathematics 2025-06-24 Jiayi Zhu , Rui Zou

The topological pressure introduced by Ruelle and similar quantities describe dynamical multifractal properties of dynamical systems. These are important characteristics of mesoscopic systems in the classical regime. Original definition of…

chao-dyn · Physics 2009-10-28 Péter Pollner , Gábor Vattay

We introduce a one-parameter family of intermediate topological pressures for nonautonomous dynamical systems which interpolate between the Pesin-Pitskel topological pressure and the lower and upper capacity pressures. The construction is…

Dynamical Systems · Mathematics 2026-05-06 Yujun Ju

Recently, Li, Li and Zhang introduced the topological pressure for correspondences and measure-theoretic entropy for transition probability kernels. Building thereon, they established a variational principle for correspondences satisfying…

Dynamical Systems · Mathematics 2025-07-08 Tao Wang

It is widely known that when $X$ is compact Hausdorff, and when $T: X \to X$ and $f: X \to \mathbb{R}$ are continuous, \begin{equation*} P(T,f) = \sup_{\text{$\mu$: Radon probability}} \left( h_\mu(T) + \int f\, \mathrm{d}\mu \right),…

Dynamical Systems · Mathematics 2016-05-09 André Caldas

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…

Dynamical Systems · Mathematics 2025-11-25 Xianqiang Li , Zhuowei Liu

Climenhaga showed the applicability of Bowen equation to arbitrary subset of a compact metric space. The main purpose of this paper is to generalize the main result of Climenhaga to free semigroup actions for non-compact sets. We introduce…

Dynamical Systems · Mathematics 2020-07-14 Qian Xiao , Dongkui Ma

Inspired to the work of Ma and Wu\cite{Ma} and Climenhaga\cite{Climenhaga}, we introduce the new nation of topological pressure of a semigroup of maps by using the Carath\'{e}odory-Pesin structure (C-P structure) with respect to arbitrary…

Dynamical Systems · Mathematics 2020-12-22 Qian Xiao , Dongkui Ma

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

Dynamical Systems · Mathematics 2009-09-15 Xianfeng Ma , Ercai Chen

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…

Dynamical Systems · Mathematics 2025-07-11 Wenhui Ma , Yun Zhao , Hanjing Zhu

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…

Dynamical Systems · Mathematics 2024-12-30 Rui Yang , Ercai Chen , Xiaoyao Zhou

Bowen introduced a definition of topological entropy of subset inspired by Hausdorff dimension in 1973 \cite{B}. In this paper we consider the Bowen's entropy for amenable group action dynamical systems and show that under the tempered…

Dynamical Systems · Mathematics 2016-02-29 Dongmei Zheng , Ercai Chen

In this paper, we introduce the unstable topological pressure for C^1-smooth partially hyperbolic diffeomorphisms with sub-additive potentials. Moreover, without any additional assumption, we have established the expected variational…

Dynamical Systems · Mathematics 2020-09-01 Wenda Zhang , Zhiqiang Li , Yunhua Zhou

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…

Dynamical Systems · Mathematics 2026-04-17 Cunyi Nan

Based on the Carath\'eodory -Pesin structure theory[11], we introduce three notions of topological pressure of a proper map and provide some properties of these notions. For the proper map of a locally compact separable metric space, we…

Dynamical Systems · Mathematics 2018-02-14 Dongkui Ma , Nuanni Fan

Recently, M. Tsukamoto (New approach to weighted topological entropy and pressure, Ergod. Theory Dyn. Syst. 43 (2023) 1004-1034) used a new approach to define the weighted topological entropy and pressure. Inspired by his ideas, we…

Dynamical Systems · Mathematics 2025-03-10 Zhengyu Yin

In this paper, we study the properties of the scaled packing topological pressures for topological dynamical system $(X,G)$, where $G$ is a countable discrete infinite amenable group. We show that the scaled packing topological pressures…

Dynamical Systems · Mathematics 2024-07-19 Zubiao Xiao , Hongwei Jia , Zhengyu Yin

Let $X$ be a compact metric space and $\Phi=\{\varphi_t\}_{t\in\mathbb{R}}$ be a continuous flow on $X$. We introduce two types of topological pressure for family of discontinuous potentials $a=\{a_t\}_{t>0}$. First, define the topological…

Dynamical Systems · Mathematics 2024-03-26 Ruolan Xiong