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学者姓名：肖祖彪
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Abstract ：
Let r≥2 and (Xi,G) (i=1,⋯,r) be topological dynamical systems with an infinite countable discrete amenable phase group G. Suppose that πi:(Xi,G)→(Xi+1,G) are factor maps, a={a1,⋯,ar−1}∈Rr−1 is a vector with 0≤ai≤1 and (w1,⋯,wr)∈Rr is a probability vector associated with a. In this paper, given f∈C(X1), we introduce the weighted topological pressure Pa(f,G). Moreover, by using measure-theoretical theory, we establish a variational principle: Pa(f,G)=supμ∈MG(X1)(∑i=1rwihμ(Xi,G)+w1∫X1fdμ), where h{⋅}(⋅,G) is the Kolmogorov-Sinai entropy of the systems acted by the amenable group G and μi=πi−1∘⋯∘π1μ is the induced G-invariant measure on Xi. © 2024 Elsevier Inc.
Keyword ：
Amenable groups Amenable groups Dynamical systems Dynamical systems Variational principle Variational principle Weighted topological entropy Weighted topological entropy Weighted topological pressure Weighted topological pressure
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| GB/T 7714 | Yin, Z. , Xiao, Z. . Variational principle of higher dimension weighted pressure for amenable group actions [J]. | Journal of Mathematical Analysis and Applications , 2024 , 538 (1) . |
| MLA | Yin, Z. 等. "Variational principle of higher dimension weighted pressure for amenable group actions" . | Journal of Mathematical Analysis and Applications 538 . 1 (2024) . |
| APA | Yin, Z. , Xiao, Z. . Variational principle of higher dimension weighted pressure for amenable group actions . | Journal of Mathematical Analysis and Applications , 2024 , 538 (1) . |
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Abstract ：
Let (X, G) be a G-system, where G is an infinite countable discrete amenable group and X is a compact metric space with a metric d. In this paper, we study the topological pressure of intricacy and average sample complexity for amenable group actions. We show that the topological pressure of strong sub-additive potential is equal to the pressure of intricacy and average sample complexity as taking supremum over open covers of X. We establish the definition of the pressure of intricacy and average sample complexity by using spanning sets and separated sets. In the last part, we show that the variational principle for pressure of intricacy and average sample complexity.
Keyword ：
Amenable group Amenable group Average sample complexity Average sample complexity Intricacy Intricacy Topological pressure Topological pressure
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| GB/T 7714 | Xiao, Zubiao , Huang, Jinna . The pressure of intricacy and average sample complexity for amenable group actions [J]. | MONATSHEFTE FUR MATHEMATIK , 2024 , 205 (2) : 391-414 . |
| MLA | Xiao, Zubiao 等. "The pressure of intricacy and average sample complexity for amenable group actions" . | MONATSHEFTE FUR MATHEMATIK 205 . 2 (2024) : 391-414 . |
| APA | Xiao, Zubiao , Huang, Jinna . The pressure of intricacy and average sample complexity for amenable group actions . | MONATSHEFTE FUR MATHEMATIK , 2024 , 205 (2) , 391-414 . |
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Abstract ：
We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups. First, for a given F(sic)lner sequence {F-n}(n=0)(+infinity), we define the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity. we also investigate the relations among these. Second, we introduce the notion of a relative dimension set. Moreover, using the method, we discuss the disjointness between the relative entropy zero extensions via the relative dimension sets of two extensions, which says that if the relative dimension sets of two extensions are different, then the extensions are disjoint.
Keyword ：
amenable groups amenable groups relative dimension sets relative dimension sets relative entropy dimensions relative entropy dimensions
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| GB/T 7714 | Xiao, Zubiao , Yin, Zhengyu . Relative entropy dimension for countable amenable group actions [J]. | ACTA MATHEMATICA SCIENTIA , 2023 , 43 (6) : 2430-2448 . |
| MLA | Xiao, Zubiao 等. "Relative entropy dimension for countable amenable group actions" . | ACTA MATHEMATICA SCIENTIA 43 . 6 (2023) : 2430-2448 . |
| APA | Xiao, Zubiao , Yin, Zhengyu . Relative entropy dimension for countable amenable group actions . | ACTA MATHEMATICA SCIENTIA , 2023 , 43 (6) , 2430-2448 . |
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Let pi : (T, X) -> (T, Z) be an extension of flows with phase group T. A point x in X is pi-distal if x is proximal to at most itself in pi(-1)pi x boolean AND (Tx) over bar under (T, X). We study the pi-distal points using combinatorial methods. We present characterizations of pi-distal points using product IP/C-w/C-recurrence, dynamics syndetic sets, distal sets, IP*-sets, and C*-sets in T. Moreover, we give the dynamics realization of IP-set of any discrete group by IP-recurrent point and the dynamics realization of C-set of Z(d) by C-recurrent point. The IP*-recurrence of pi-distal points introduced here is useful for simplifying the proof of Furstenberg's structure theorem. (C) 2021 Elsevier B.V. All rights reserved.
Keyword ：
C-set C-set C-w-set C-w-set Distal point Distal point Flow Flow IP-set IP-set Product recurrence Product recurrence
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| GB/T 7714 | Dai, Xiongping , Liang, Hailan , Xiao, Zubiao . Characterizations of relativized distal points of topological dynamical systems [J]. | TOPOLOGY AND ITS APPLICATIONS , 2021 , 302 . |
| MLA | Dai, Xiongping 等. "Characterizations of relativized distal points of topological dynamical systems" . | TOPOLOGY AND ITS APPLICATIONS 302 (2021) . |
| APA | Dai, Xiongping , Liang, Hailan , Xiao, Zubiao . Characterizations of relativized distal points of topological dynamical systems . | TOPOLOGY AND ITS APPLICATIONS , 2021 , 302 . |
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