相关论文: New approach to weighted topological entropy and p…

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…

In [D. Feng, W. Huang, Variational principle for weighted topological pressure. J. Math. Pures Appl. (2016)], the authors studied weighted topological pressure and established a variational principle for it. In this paper, we introduce the…

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…

In this paper, we investigate the relations between various types of topological pressures and different versions of measure-theoretical pressures. We extend Feng- Huang's variational principle for packing entropy to packing pressure and…

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…

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…

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),…

Tsukamoto (2022) introduced the notion of Bedford-McMullen carpet system, a subsystem of $([0,1]^{\mathbb{N}}\times[0,1]^{\mathbb{N}},shift)$ whose metric mean dimension and mean Hausdorff dimension does not coincide in general. The aim of…

Let $\boldsymbol{X}=\{X_{k}\}_{k=0}^{\infty}$ be a sequence of compact metric spaces $X_{k}$ and $\boldsymbol{T}=\{T_{k}\}_{k=0}^{\infty}$ a sequence of continuous mappings $T_{k}:X_{k} \to X_{k+1}$. The pair…

In 1984 Bedford and McMullen independently introduced a family of self-affine sets now known as \emph{Bedford-McMullen carpets}. Their work stimulated a lot of research in the areas of fractal geometry and non-conformal dynamics. In this…

This study focuses on the topological pressure of nonautonomous iterated function systems defined on a compact metric space. We establish an inequality relating two topological pressures associated with a factor map of nonautonomous…

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…

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…

Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…

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.…

This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…

In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…

We introduce a pseudo entropy extension of topological entanglement entropy called topological pseudo entropy. Various examples of the topological pseudo entropies are examined in three-dimensional Chern-Simons gauge theory with Wilson loop…

We give a new definition of topological pressure for arbitrary (non-compact, non-invariant) Borel subsets of metric spaces. This new quantity is defined via a suitable variational principle, leading to an alternative definition of an…