We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups.First,for a given Følner sequence,we define the relative entropy dimensions and the dimen...We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups.First,for a given Følner sequence,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.展开更多
In this paper,we study the proximal relation,regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions.A useful tool is the support of a topological dynamic...In this paper,we study the proximal relation,regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions.A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation,and we prove that above three relations all coincide on a Banach mean equicontinuous system generated by an amenable group action.展开更多
In this paper,we study the properties of the scaled packing topological pressures for a topological dynamical system(X,G),where G is a countable discrete infinite amenable group.We show that the scaled packing topolog...In this paper,we study the properties of the scaled packing topological pressures for a topological dynamical system(X,G),where G is a countable discrete infinite amenable group.We show that the scaled packing topological pressures can be determined by the scaled Bowen topological pressures.We obtain Billingsley’s Theorem for the scaled packing pressures with a G-action.Then we get a variational principle between the scaled packing pressures and the scaled measure-theoretic upper local pressures.Finally,we give some restrictions on the scaled sequence b,then in the case of the set Xμof generic points,we prove thatP^(P)(X_(μ),{F_(n)},f,b)=h_(μ)(X)+∫_(X)∫dμ,if(F(n))is tempered andμis a G-invariant ergodic Borel probability measure.展开更多
In this paper,we study the Bowen entropy of stable sets in positive entropy G-system of amenable group actions.The lower bound of the Bowen entropy of these sets are estimated.
In 2018,Petersen and Wilson introduced the notion of dynamical intricacy and average sample complexity for dynamical systems of Z-action,based on the past works on the notion of intricacy in the research of brain netw...In 2018,Petersen and Wilson introduced the notion of dynamical intricacy and average sample complexity for dynamical systems of Z-action,based on the past works on the notion of intricacy in the research of brain network and probability theory.If one wants to take into account underlying system geometry in applications,more general group actions may need to be taken into consideration.In this paper,we consider this notion in the case of amenable group actions.We show that many basic properties in the Z-action case remain true.We also show that their suprema over covers or partitions are equal to the amenable topological entropy and the measure entropy,using the quasitiling technique in the theory of the amenable group.展开更多
In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation betw...In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation between local measure-theoretic polynomial entropy of Borel probability measures and polynomial entropy on an arbitrary subset. Also, we establish a variational principle for polynomial entropy on compact subsets in the context of amenable group actions.展开更多
Exploring the creation of comfortable objects in traditional tourism villages from the perspective of tourists can help reveal the essence of these amenities.Taking Yidoushui Ancient Village in Jiaozuo City,Henan Prov...Exploring the creation of comfortable objects in traditional tourism villages from the perspective of tourists can help reveal the essence of these amenities.Taking Yidoushui Ancient Village in Jiaozuo City,Henan Province as an example,this study applied the five-element theory of rural amenities to the research on the tourism-oriented traditional villages.With the help of text analysis tools and field investigations,it identified the objects,indicators,and elements of amenities in Yidoushui Ancient Village.Based on this framework,a survey questionnaire was designed for field research,followed by data analysis.The results indicated that tourists primarily focused on ecological amenities in traditional tourism villages;overall,visitors exhibited relative high perception and positive evaluation of the amenities;there were significant differences in the impact of different amenities indicators on tourist experience,and multiple indicators of ecological amenities showed significantly positive correlation with tourists’mood,satisfaction,and revisit intention,making them core factors in enhancing tourist experience.Cultural amenities significantly improved mood and satisfaction,but showed no significant effect on revisit intention.展开更多
Adequate,safe and affordable housing and basic services for all are the basis for sustainable development,livelihood security and basic housing rights.Shelter is a basic human rights guarantee and improvements in livi...Adequate,safe and affordable housing and basic services for all are the basis for sustainable development,livelihood security and basic housing rights.Shelter is a basic human rights guarantee and improvements in living conditions are of significant importance to the quality of life.The article uses data from China’s fifth,sixth and seventh population censuses to reveal the spatial and temporal differences in the improvement of housing conditions of households in 281 cities in China from 2000 to 2020.The study concludes the following:(i)The housing conditions score of urban households in China has improved significantly,and the living environment has been significantly improved.The center of gravity of the overall housing conditions score shifts from the western region to the eastern region and then to the central region.(ii)The housing facilities in China’s cities have become increasingly sophisticated during the study period.The overall variation in housing amenities tends to decrease overall,with higher intra-belt variation than inter-belt variation in the four main regions.(iii)Self-built housing,rented housing,purchased housing,other types of housing and inherited housing are the main sources of housing for urban househ olds in China.From 2000 to 2020,the housing structure is characterized by two increases and one decrease,namely an increase in the proportion of purchased and rented housing and a decrease in the proportion of self-built housing.(iv)The main factors influencing the improvement of housing conditions are historical factors,the forces of marketization,urbanization,and housing policy.展开更多
Let G be a countable discrete infinite amenable group which acts continuously on a compact metric space X and let μ be an ergodic G-invariant Borel probability measure on X. For a fixed tempered F?lner sequence {Fn} ...Let G be a countable discrete infinite amenable group which acts continuously on a compact metric space X and let μ be an ergodic G-invariant Borel probability measure on X. For a fixed tempered F?lner sequence {Fn} in G with limn→+∞|Fn|/log n= ∞, we prove the following result:h_top^B(G_μ, {F_n}) = h_μ(X, G),where G_μ is the set of generic points for μ with respect to {F_n} and h_top^B(G_μ, {F_n}) is the Bowen topological entropy(along {F_n}) on G_μ. This generalizes the classical result of Bowen(1973).展开更多
Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric g...Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric group actions on both of them,if X is coarsely embeddable into H and the group is amenable,then the coarse embedding can be modified to be equivariant by using the invariant mean property of the amenable group.展开更多
基金supported by the NNSF of China (12201120,12171233)the Educational Research Project for Young and Middle-aged Teachers of Fujian Province (JAT200045).
文摘We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups.First,for a given Følner sequence,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.
基金supported by NSF of China(11671057)NSF of Chongqing(cstc2020jcyj-msxm X0694)the Fundamental Research Funds for the Central Universities(2018CDQYST0023)。
文摘In this paper,we study the proximal relation,regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions.A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation,and we prove that above three relations all coincide on a Banach mean equicontinuous system generated by an amenable group action.
基金supported by the NNSF of China(12201120)the visiting fellowships supported by Fujian Alliance of Mathematics while visiting Xiamen University in the winter of 2023。
文摘In this paper,we study the properties of the scaled packing topological pressures for a topological dynamical system(X,G),where G is a countable discrete infinite amenable group.We show that the scaled packing topological pressures can be determined by the scaled Bowen topological pressures.We obtain Billingsley’s Theorem for the scaled packing pressures with a G-action.Then we get a variational principle between the scaled packing pressures and the scaled measure-theoretic upper local pressures.Finally,we give some restrictions on the scaled sequence b,then in the case of the set Xμof generic points,we prove thatP^(P)(X_(μ),{F_(n)},f,b)=h_(μ)(X)+∫_(X)∫dμ,if(F(n))is tempered andμis a G-invariant ergodic Borel probability measure.
基金Supported by NSFC(No.11861010),also supported by NSFC(No.12171175),also supported by NSFC(No.12261006)NSF of Guangxi Province(No.2018GXNSFFA281008)Project of Guangxi First Class Disciplines of Statistics(No.GJKY-2022-01)。
文摘In this paper,we study the Bowen entropy of stable sets in positive entropy G-system of amenable group actions.The lower bound of the Bowen entropy of these sets are estimated.
基金supported by National Natural Science Foundation of China(Grant No.11701231)supported by National Natural Science Foundation of China(Grant Nos.11801584 and 11871228)+1 种基金National Science Foundation of Jiangsu Province(Grant No.BK20170225)Science Foundation of Jiangsu Normal University(Grant No.17XLR011)。
文摘In 2018,Petersen and Wilson introduced the notion of dynamical intricacy and average sample complexity for dynamical systems of Z-action,based on the past works on the notion of intricacy in the research of brain network and probability theory.If one wants to take into account underlying system geometry in applications,more general group actions may need to be taken into consideration.In this paper,we consider this notion in the case of amenable group actions.We show that many basic properties in the Z-action case remain true.We also show that their suprema over covers or partitions are equal to the amenable topological entropy and the measure entropy,using the quasitiling technique in the theory of the amenable group.
基金supported by Foundation in higher education institutions of He’nan Province,P. R. China(Grant No. 23A110020)National Natural Science Foundation of China (Grant No. 11401363)+4 种基金the Foundation for the Training of Young Key Teachers in Colleges and Universities in He’nan Province,P. R. China (Grant No.2018GGJS134)supported by National Natural Science Foundation of China (Gratn No.11971236)China Postdoctoral Science Foundation (Grant No. 2016M591873)China Postdoctoral Science Special Foundation (Grant No. 2017T100384)funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability measure on a compact metric space,and investigate the relation between local measure-theoretic polynomial entropy of Borel probability measures and polynomial entropy on an arbitrary subset. Also, we establish a variational principle for polynomial entropy on compact subsets in the context of amenable group actions.
基金Sponsored by Humanities and Social Sciences Research Planning Fund of the Ministry of Education of China(23YJAZH171)Philosophy and Social Sciences Project of Henan Province,China(2024XWH099).
文摘Exploring the creation of comfortable objects in traditional tourism villages from the perspective of tourists can help reveal the essence of these amenities.Taking Yidoushui Ancient Village in Jiaozuo City,Henan Province as an example,this study applied the five-element theory of rural amenities to the research on the tourism-oriented traditional villages.With the help of text analysis tools and field investigations,it identified the objects,indicators,and elements of amenities in Yidoushui Ancient Village.Based on this framework,a survey questionnaire was designed for field research,followed by data analysis.The results indicated that tourists primarily focused on ecological amenities in traditional tourism villages;overall,visitors exhibited relative high perception and positive evaluation of the amenities;there were significant differences in the impact of different amenities indicators on tourist experience,and multiple indicators of ecological amenities showed significantly positive correlation with tourists’mood,satisfaction,and revisit intention,making them core factors in enhancing tourist experience.Cultural amenities significantly improved mood and satisfaction,but showed no significant effect on revisit intention.
基金Project of Philosophy and Social Science of Shanghai“Study on the Role of Population Ageing on Economic Growth in the Yangtze River Delta Urban Agglomeration”(2023ZSH002).
文摘Adequate,safe and affordable housing and basic services for all are the basis for sustainable development,livelihood security and basic housing rights.Shelter is a basic human rights guarantee and improvements in living conditions are of significant importance to the quality of life.The article uses data from China’s fifth,sixth and seventh population censuses to reveal the spatial and temporal differences in the improvement of housing conditions of households in 281 cities in China from 2000 to 2020.The study concludes the following:(i)The housing conditions score of urban households in China has improved significantly,and the living environment has been significantly improved.The center of gravity of the overall housing conditions score shifts from the western region to the eastern region and then to the central region.(ii)The housing facilities in China’s cities have become increasingly sophisticated during the study period.The overall variation in housing amenities tends to decrease overall,with higher intra-belt variation than inter-belt variation in the four main regions.(iii)Self-built housing,rented housing,purchased housing,other types of housing and inherited housing are the main sources of housing for urban househ olds in China.From 2000 to 2020,the housing structure is characterized by two increases and one decrease,namely an increase in the proportion of purchased and rented housing and a decrease in the proportion of self-built housing.(iv)The main factors influencing the improvement of housing conditions are historical factors,the forces of marketization,urbanization,and housing policy.
基金supported by National Basic Research Program of China (Grant No. 2013CB834100)National Natural Science Foundation of China (Grant Nos. 11271191 and 11431012)
文摘Let G be a countable discrete infinite amenable group which acts continuously on a compact metric space X and let μ be an ergodic G-invariant Borel probability measure on X. For a fixed tempered F?lner sequence {Fn} in G with limn→+∞|Fn|/log n= ∞, we prove the following result:h_top^B(G_μ, {F_n}) = h_μ(X, G),where G_μ is the set of generic points for μ with respect to {F_n} and h_top^B(G_μ, {F_n}) is the Bowen topological entropy(along {F_n}) on G_μ. This generalizes the classical result of Bowen(1973).
基金Supported by National Natural Science Foundation of China(11871342)。
文摘Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric group actions on both of them,if X is coarsely embeddable into H and the group is amenable,then the coarse embedding can be modified to be equivariant by using the invariant mean property of the amenable group.
