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35 results on '"Cheng, Wen-Chiao"'

2. On the hitting probabilities of limsup random fractals

Author

Hu, Zhang-nan, Cheng, Wen-Chiao, and Li, Bing

Subjects
Mathematics - Probability
Abstract

Let $A$ be a limsup random fractal with indices $\gamma_1, ~\gamma_2 ~$and $\delta$ on $[0,1]^d$. We determine the hitting probability $\mathbb{P}(A\cap G)$ for any analytic set $G$ with the condition $(\star)$$\colon$ $\dim_{\rm H}(G)>\gamma_2+\delta$, where $\dim_{\rm H}$ denotes the Hausdorff dimension. This extends the correspondence of Khoshnevisan, Peres and Xiao [10] by relaxing the condition that the probability $P_n$ of choosing each dyadic hyper-cube is homogeneous and $\lim\limits_{n\to\infty}\frac{\log_2P_n}{n}$ exists. We also present some counterexamples to show the Hausdorff dimension in condition $(\star)$ can not be replaced by the packing dimension., Comment: 12 pages

Published
2021
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6. Variational principles for topological pressures on subsets

Author

Tang, Xinjia, Cheng, Wen-Chiao, and Zhao, Yun

Subjects
Mathematics - Dynamical Systems, 37D35, 37A35, 37C45
Abstract

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 known results of topological pressure. More precisely, the investigation of the variational principle is given and related propositions are also described. That is, this paper defines the measure theoretic pressure $P_{\mu}(T,f)$ for any $\mu\in{\mathcal M(X)}$, and shows that $P_B(T,f,K)=\sup\bigr\{P_{\mu}(T,f):{\mu}\in{\mathcalM(X)},{\mu}(K)=1\bigr\}$, where $K\subseteq X$ is a non-empty compact subset and $P_B(T,f,K)$ is the Bowen topological pressure on $K$. Furthermore, if $Z\subseteq X$ is an analytic subset, then $P_B(T,f,Z)=\sup\bigr\{P_B(T,f,K):K\subseteq Z\ \text{is compact}\bigr\}$. However, this analysis relies on more techniques of ergodic theory and topological dynamics., Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1012.1103, arXiv:1111.7121 by other authors

Published
2013

7. Pressures for Asymptotically Sub-additive Potentials Under a Mistake Function

Author

Cheng, Wen-Chiao, Zhao, Yun, and Cao, Yongluo

Subjects
Mathematics - Dynamical Systems, 37D35, 37A35
Abstract

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 reveals a variational principle for the new defined topological pressure without any additional conditions on the potentials and the compact metric space., Comment: 13pages

Published
2010

20. Q-entropy for general topological dynamical systems.

Author

Zhao, Yun, Cheng, Wen-Chiao, and Ho, Chih-Chang

Subjects
TOPOLOGICAL entropy, DYNAMICAL systems, ERGODIC theory, CONTINUOUS functions, PROBABILITY measures
Abstract

The aim of this paper is to extend the q-entropy from symbolic systems to a general topological dynamical system. Using a (weak) Gibbs measure as the reference measure, this paper defines q-topological entropy and q-metric entropy, then studies basic properties of these entropies. In particular, this paper describes the relations between q-topological entropy and topological pressure for almost additive potentials, and the relations between q-metric entropy and local metric entropy. Although these relations are quite similar to that described in [19], the methods used here need more techniques from the theory of thermodynamic formalism with almost additive potentials. [ABSTRACT FROM AUTHOR]

Published
2019
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21. Some properties on topological entropy of free semigroup action.

Author

Tang, Jingru, Li, Bing, and Cheng, Wen-Chiao

Subjects
TOPOLOGICAL entropy, FREE groups, POWER law (Mathematics), SKEWNESS (Probability theory), MATHEMATICAL transformations
Abstract

The aim of this paper is to examine the topological entropy for a free semigroup action defined by Bufetov using separated and spanning sets. First, this study reveals that such entropy is a topological conjugacy invariant and also can be equivalently defined using open covers. Furthermore, a quantitative analogue of Bowen's theorem for semiconjugacy is provided and we compared the topological entropies presented by Bufetov and Biś. Finally, a formula for the entropy of skew-product transformation with respect to the subshift is obtained. [ABSTRACT FROM PUBLISHER]

Published
2018
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34. COSET PRESSURE WITH SUB-ADDITIVE POTENTIALS.

Author

ZHAO, YUN and CHENG, WEN-CHIAO

Subjects
*VARIATIONAL principles, *ENTROPY, *APPROXIMATION theory, *TOPOLOGICAL dynamics, *ERGODIC theory, *STATISTICAL mechanics
Abstract

The goal of this paper is to define the coset topological pressure for sub-additive potentials via separated sets on a compact metric group. Analogues of basic properties for topological pressure hold. This study also reveals a variational principle for the coset topological pressure. The process of the proof is quite similar to that of Cao, Feng and Huang's approximations, but the analysis needs more techniques of ergodic theory and topological dynamics. [ABSTRACT FROM AUTHOR]

Published
2014
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35. Tail pressure and the tail entropy function.

Author

LI, YUAN, CHEN, ERCAI, and CHENG, WEN-CHIAO

Subjects
TOPOLOGICAL entropy, VARIATIONAL principles, MATHEMATICAL transformations, TOPOLOGICAL dynamics, INVARIANT measures, MATHEMATICAL analysis
Abstract

Burguet [A direct proof of the tail variational principle and its extension to maps. Ergod. Th. & Dynam. Sys.29 (2009), 357–369] presented a direct proof of the variational principle of tail entropy and extended Downarowicz’s results to a non-invertible case. This paper defines and discusses tail pressure, which is an extension of tail entropy for continuous transformations. This study reveals analogs of many known results of topological pressure. Specifically, a variational principle is provided and some applications of tail pressure, such as the investigation of invariant measures and equilibrium states, are also obtained. [ABSTRACT FROM PUBLISHER]

Published
2012
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