Bowen entropy of sets of generic points for fixed-point free flows

Wang, Yunping; Chen, Ercai; Lin, Zijie; Wu, Ting

doi:10.1016/j.jde.2020.07.008

Cited by 8 publications

(7 citation statements)

References 17 publications

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“…To establish the variation principle for generic set G µ , we follow the strategies of [11,Theorem 4.1] and [18,Theorem 1.3]. Since P (φ, •) ≤ P (φ, •), we shall prove that h µ (ϕ 1 ) + φ dµ is an upper bound of P (φ, G µ ).…”

Section: Variational Principle For P (φ G µ )mentioning

confidence: 99%

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Topological pressure on subsets for fixed-point free flows

Wang

2022

Preprint

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Section: Variational Principle For P (φ G µ )mentioning

confidence: 99%

“…[7] defined the Bowen topological entropy by reparametrization and established its variational principle with local entropy on subsets. Later it was further studied in [8,18].…”

mentioning

confidence: 99%

Topological pressure on subsets for fixed-point free flows

Wang

2022

Preprint

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“…in [2] introduced Bowen topological entropy for flows via the reparametrization balls and proved the variational principle (1.1) for flows without fixed-points. For further studies on Bowen topological entropy for fixed-point free flows, see [5,11]. In the present paper, we will study packing topological entropy for fixed-point free flows.…”

Section: Introductionmentioning

confidence: 99%

Packing entropy for fixed-point free flows

Liu¹,

Lei²

2021

Preprint

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Let (X, φ) be a compact flow without fixed points. We define the packing topological entropy h P top (φ, K) on subsets of X through considering all the possible reparametrizations of time. For fixed-point free flows, we prove the following result: for any non-empty compact subset K of X,, µ is a Borel probability measure onX}, where h µ (φ) denotes the upper local entropy for a Borel probability measure µ on X.

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“…Later, Zhao et al [ZCZ18] generalized this result to weighted Bowen topological entropy. The versions of amenable group and fixed-point free flows can be founded in [ZC18,WCL20], respectively. If µ ∈ M(X, T ), Pfister and Sullivan showed that the equality h top (T, G µ ) = h µ (T ) still holds under the condition of the g-almost product property, and this work was extended to amenable group by Zhang [Z18] by using quasi-tiling method.…”

Section: Introductionmentioning

confidence: 99%

Packing metric mean dimension of sets of generic points

Yang¹,

Chen²,

Zhou³

2022

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We first establish a mean version of Katok's entropy formula in this paper, which is an analogue of the classical Katok's entropy formula. Then we establish two new variational principles for Bowen upper metric mean dimension and packing upper metric mean dimension on subsets in terms of two measure-theoretic quantities related to Katok's entropy defined by Carathēodory-Pesin structures. Finally, we obtain a new formula of packing metric mean dimension of generic points of ergodic measures without additional conditions compared with our previous work [YCZ22]. Additionally, we obtain inverse variational principles for packing metric mean dimension.

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Bowen entropy of sets of generic points for fixed-point free flows

Cited by 8 publications

References 17 publications

Topological pressure on subsets for fixed-point free flows

Topological pressure on subsets for fixed-point free flows

Packing entropy for fixed-point free flows

Packing metric mean dimension of sets of generic points

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