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学者姓名：肖祖彪
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Abstract ：
Let r >= 2 and (X-i,G) (i=1,center dot center dot center dot,r) be topological dynamical systems with an infinite countable discrete amenable phase group G. Suppose that pi(i):(X-i,G)->(Xi+1,G) are factor maps, a={a(1),center dot center dot center dot,a(r-1)}is an element of Rr-1 is a vector with 0 <= a(i) <= 1 and (w(1),center dot center dot center dot,w(r))is an element of R-r is a probability vector associated with a. In this paper, given f is an element of C(X1), we introduce the weighted topological pressure P-a(f,G). Moreover, by using measure-theoretical theory, we establish a variational principle: P-a(f,G)=sup(mu is an element of M)(G)((X)1)(Sigma(r)(i=1)w(i)h(mu)i(X-i,G)+w(1)integral(X)1fd mu), where h({center dot})(center dot,G) is the Kolmogorov-Sinai entropy of the systems acted by the amenable group G and mu(i)=pi(i-1)circle center dot center dot center dot circle pi(1)mu is the induced G-invariant measure on X-i.
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, Zhengyu , Xiao, Zubiao . Variational principle of higher dimension weighted pressure for amenable group actions [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2024 , 538 (1) . |
| MLA | Yin, Zhengyu 等. "Variational principle of higher dimension weighted pressure for amenable group actions" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 538 . 1 (2024) . |
| APA | Yin, Zhengyu , Xiao, Zubiao . 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 G be an infinite countable amenable group and P a polyhedron with the topological dimension dim(P) < infinity. We construct a minimal subshift (X, G) of (P-G, G) such that its mean topological dimension is equal to dim(P). This result answers the question of Dou (2017 Discrete Contin. Dyn. Syst. 37 1411-24). Moreover, it extends the work of Jin and Qiao (2023 arXiv:2102.10339) for Z-action.
Keyword ：
amenable groups amenable groups dynamical systems dynamical systems mean topological dimension mean topological dimension minimal subshifts minimal subshifts tiling tiling
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| GB/T 7714 | Yin, Zhengyu , Xiao, Zubiao . Minimal amenable subshift with full mean topological dimension [J]. | NONLINEARITY , 2024 , 37 (11) . |
| MLA | Yin, Zhengyu 等. "Minimal amenable subshift with full mean topological dimension" . | NONLINEARITY 37 . 11 (2024) . |
| APA | Yin, Zhengyu , Xiao, Zubiao . Minimal amenable subshift with full mean topological dimension . | NONLINEARITY , 2024 , 37 (11) . |
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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 ：
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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