Related papers: Topological pressure for discontinuous semiflows a…
Feng--Huang (2016) introduced weighted topological entropy and pressure for factor maps between dynamical systems and established its variational principle. Tsukamoto (2022) redefined those invariants quite differently for the simplest case…
Motivated by the notion of topological entropy for free semigroup actions introduced by Bi\'s, we define the Pesin--Pitskel topological pressure for non-autonomous iterated function systems via the Carath\'eodory--Pesin structure. We show…
This article establishes the variational principle of topological pressure for actions of sofic groupoids.
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…
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 defines the pressure for asymptotically subadditive potentials under a mistake function, including the measuretheoretical and the topological versions. Using the advanced techniques of ergodic theory and topological dynamics, we…
We consider impulsive semiflows and establish sufficient conditions to the existence of invariant measures. Namely, the impulsive set and its image are both submanifolds of codimension one that are transversal to the flow direction.…
Multifractal analysis studies level sets of asymptotically defined quantities in a topological dynamical system. We consider the topological pressure function on such level sets, relating it both to the pressure on the entire phase space…
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…
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…
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 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…
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 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…
We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…
We introduce the notion of localized topological pressure for continuous maps on compact metric spaces. The localized pressure of a continuous potential $\varphi$ is computed by considering only those $(n,\epsilon)$-separated sets whose…
In this paper, we introduce the notions of topological pressure and measure-theoretic entropy for a free semigroup action. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action, we assign a…
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…
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…
Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail…