Related papers: Variational Principles For BS Dimension of Subsets
We aim to investigate the dimension theory of $\alpha$-pressure-like quantities. By means of the Carath$\acute{\rm e}$odory-Pesin structure, we define $\alpha$-BS dimension and $\alpha$-Pesin topological pressure on subsets using…
In this manuscript, we focus on the investigation of the BS dimension and BS packing dimension under amenable group actions. Firstly, we obtain a Bowen's equation which illustrate the relation of BS packing dimension to the packing…
In this note, we show several variational principles for metric mean dimension. First we prove a variational principles in terms of Shapira's entropy related to finite open covers. Second we establish a variational principle in terms of…
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…
Firstly, we introduce a new notion called induced upper metric mean dimension with potential, which naturally generalizes the definition of upper metric mean dimension with potential given by Tsukamoto to more general cases, then 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…
In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carath\'{e}odory dimension characteristic, motivated by the work of Bowen and Pesin etc. We…
We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic measures. Second we derive a variational principle for…
We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entropy of the underlying system. Our results hold for dynamical…
We prove a variational principle for the upper and lower metric mean dimension of level sets \[ \left\{x\in X: \lim_{n\to\infty}\frac{1}{n}\sum_{j=0}^{n-1}\varphi(f^{j}(x))=\alpha\right\} \] associated to continuous potentials $\varphi:X\to…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
In this paper we introduce three notions of measure theoretical entropy of a measurable cover U in a measure theoretical dynamical system. Two of them were already introduced in [R] and the new one is defined only in the ergodic case. We…
In this article, we introduce a notion of relative mean metric dimension with potential for a factor map $\pi: (X,d, T)\to (Y, S)$ between two topological dynamical systems. To link it with ergodic theory, we establish four variational…
We aim to establish Bowen's equations for upper capacity invariance pressure and Pesin-Pitskel invariance pressure of discrete-time control systems. We first introduce a new invariance pressure called induced invariance pressure on…
It is well-known that the relativized variational principle established by Bogenschutz and Kifer connects the fiber topological entropy and fiber measure-theoretic entropy. In context of random dynamical systems, metric mean dimension was…
Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as $$B_n(x,e^{-n\epsilon})=\{y\in X: d(T^jx, T^jy)<e^{-n\epsilon}, \forall 0\leq j\leq n-1\}.$$ We introduce the notion of neutralized Bowen topological entropy of subsets by…
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 chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
In this paper, we introduce mean dimension quantities with sub-additive potentials. We define mean dimension with sub-additive potentials and mean metric dimension with sub-additive potentials, and establish a double variational principle…
This paper defines and discusses the dimension notion of topological slow entropy of any subset for Z^d actions. Also, the notion of measure-theoretic slow entropy for Z^d actions is presented, which is modified from Brin and Katok [2].…