ON DISTRIBUTIONAL n-CHAOS
Let （X, f ） be a topological dynamical system, where X is a nonempty compact and metrizable space with the metric d and f ：X →X is a continuous map. For any integer n≥2, denote the product space by X（n）=X · · · × X｜ {z }n times . We say a system （X, f ） is generally distributionally n-chaotic if the...
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| Veröffentlicht in: | Acta mathematica scientia 2014-09, Vol.34 (5), p.1473-1480 |
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| creator | 谭枫 符和满 |
| description | Let （X, f ） be a topological dynamical system, where X is a nonempty compact and metrizable space with the metric d and f ：X →X is a continuous map. For any integer n≥2, denote the product space by X（n）=X · · · × X｜ {z }n times . We say a system （X, f ） is generally distributionally n-chaotic if there exists a residual set D ？X（n） such that for any point x=（x1, · · · , xn）∈D, lim inf k→∞#（{i：0≤i≤k-1, min{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ0}） k=0 for some real numberδ0〉0 and lim sup k→∞#（{i：0≤i≤k-1, max{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ}） k=1 for any real number δ 〉 0, where #（·） means the cardinality of a set. In this paper, we show that for each integer n ≥ 2, there exists a system （X,σ） which satisfies the following conditions： （1） （X,σ） is transitive;（2） （X,σ） is generally distributionally n-chaotic, but has no distributionally （n＋1）-tuples;（3） the topological entropy of （X,σ） is zero and it has an IT-tuple. |
| doi_str_mv | 10.1016/S0252-9602(14)60097-7 |
| format | Article |
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For any integer n≥2, denote the product space by X（n）=X · · · × X｜ {z }n times . We say a system （X, f ） is generally distributionally n-chaotic if there exists a residual set D ？X（n） such that for any point x=（x1, · · · , xn）∈D, lim inf k→∞#（{i：0≤i≤k-1, min{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ0}） k=0 for some real numberδ0〉0 and lim sup k→∞#（{i：0≤i≤k-1, max{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ}） k=1 for any real number δ 〉 0, where #（·） means the cardinality of a set. In this paper, we show that for each integer n ≥ 2, there exists a system （X,σ） which satisfies the following conditions： （1） （X,σ） is transitive;（2） （X,σ） is generally distributionally n-chaotic, but has no distributionally （n＋1）-tuples;（3） the topological entropy of （X,σ） is zero and it has an IT-tuple.</description><identifier>ISSN: 0252-9602</identifier><identifier>EISSN: 1572-9087</identifier><identifier>DOI: 10.1016/S0252-9602(14)60097-7</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>distributional chaos ; Dynamical systems ; Dynamics ; Entropy ; Integers ; LIM ; Real numbers ; Topology ; transitive systems ; 分配 ; 可度量空间 ; 拓扑动力系统 ; 拓扑熵 ; 整数 ; 映射 ; 集合</subject><ispartof>Acta mathematica scientia, 2014-09, Vol.34 (5), p.1473-1480</ispartof><rights>2014 Wuhan Institute of Physics and Mathematics</rights><rights>Copyright © Wanfang Data Co. Ltd. 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For any integer n≥2, denote the product space by X（n）=X · · · × X｜ {z }n times . We say a system （X, f ） is generally distributionally n-chaotic if there exists a residual set D ？X（n） such that for any point x=（x1, · · · , xn）∈D, lim inf k→∞#（{i：0≤i≤k-1, min{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ0}） k=0 for some real numberδ0〉0 and lim sup k→∞#（{i：0≤i≤k-1, max{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ}） k=1 for any real number δ 〉 0, where #（·） means the cardinality of a set. In this paper, we show that for each integer n ≥ 2, there exists a system （X,σ） which satisfies the following conditions： （1） （X,σ） is transitive;（2） （X,σ） is generally distributionally n-chaotic, but has no distributionally （n＋1）-tuples;（3） the topological entropy of （X,σ） is zero and it has an IT-tuple.</description><subject>distributional chaos</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Entropy</subject><subject>Integers</subject><subject>LIM</subject><subject>Real numbers</subject><subject>Topology</subject><subject>transitive systems</subject><subject>分配</subject><subject>可度量空间</subject><subject>拓扑动力系统</subject><subject>拓扑熵</subject><subject>整数</subject><subject>映射</subject><subject>集合</subject><issn>0252-9602</issn><issn>1572-9087</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqFkEtPwkAUhSdGExH9AS5MiCtYVOddujKID5oQmgisJ53pFIeUFmZA8N87pejW1UxuvnPPPQeAOwQfEET8cQoxw0HEIe4i2uMQRmEQnoEWYqEfw354Dlp_yCW4cm4JvQ5z2gK3yaTzEk9nH_HzfBYnk8G4UwbD0SCZXoOLPC2cvjm9bTB_e50NR8E4eY-Hg3GgKCTbII2wyhkmNA0jwoj_Uik5z1jkz8gJ47KeSY9JSSOpIMKaSE1UphVFXJM26DV792mZp-VCLKudLb2jcId9cZBCY4goZD6WZ7sNu7bVZqfdVqyMU7oo0lJXOycQ4yHs04iEHmUNqmzlnNW5WFuzSu23QFDUtYljbaLuRCAqjrWJWvfU6LTP_GW0FU4ZXSqdGavVVmSV-XfD_cn5syoXG-Mj_Vpz7gUcE05-AH5reuc</recordid><startdate>20140901</startdate><enddate>20140901</enddate><creator>谭枫 符和满</creator><general>Elsevier Ltd</general><general>School of the mathematical science, South China Normal University, Guangzhou 510631, China%College of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing 526061, China</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20140901</creationdate><title>ON DISTRIBUTIONAL n-CHAOS</title><author>谭枫 符和满</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c403t-a92cf5234a79353f524bb66d59097f356b3f52ba92bb49bc012e3be3cdec416e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>distributional chaos</topic><topic>Dynamical systems</topic><topic>Dynamics</topic><topic>Entropy</topic><topic>Integers</topic><topic>LIM</topic><topic>Real numbers</topic><topic>Topology</topic><topic>transitive systems</topic><topic>分配</topic><topic>可度量空间</topic><topic>拓扑动力系统</topic><topic>拓扑熵</topic><topic>整数</topic><topic>映射</topic><topic>集合</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>谭枫 符和满</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Acta mathematica scientia</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>谭枫 符和满</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ON DISTRIBUTIONAL n-CHAOS</atitle><jtitle>Acta mathematica scientia</jtitle><addtitle>Acta Mathematica Scientia</addtitle><date>2014-09-01</date><risdate>2014</risdate><volume>34</volume><issue>5</issue><spage>1473</spage><epage>1480</epage><pages>1473-1480</pages><issn>0252-9602</issn><eissn>1572-9087</eissn><abstract>Let （X, f ） be a topological dynamical system, where X is a nonempty compact and metrizable space with the metric d and f ：X →X is a continuous map. For any integer n≥2, denote the product space by X（n）=X · · · × X｜ {z }n times . We say a system （X, f ） is generally distributionally n-chaotic if there exists a residual set D ？X（n） such that for any point x=（x1, · · · , xn）∈D, lim inf k→∞#（{i：0≤i≤k-1, min{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ0}） k=0 for some real numberδ0〉0 and lim sup k→∞#（{i：0≤i≤k-1, max{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ}） k=1 for any real number δ 〉 0, where #（·） means the cardinality of a set. In this paper, we show that for each integer n ≥ 2, there exists a system （X,σ） which satisfies the following conditions： （1） （X,σ） is transitive;（2） （X,σ） is generally distributionally n-chaotic, but has no distributionally （n＋1）-tuples;（3） the topological entropy of （X,σ） is zero and it has an IT-tuple.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/S0252-9602(14)60097-7</doi><tpages>8</tpages></addata></record> |
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| source | Elsevier ScienceDirect Journals; Alma/SFX Local Collection |
| subjects | distributional chaos Dynamical systems Dynamics Entropy Integers LIM Real numbers Topology transitive systems 分配 可度量空间 拓扑动力系统 拓扑熵 整数 映射 集合 |
| title | ON DISTRIBUTIONAL n-CHAOS |
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