由双Furstenberg族诱导的混沌

吴新星, 朱培勇

数学学报 ›› 2012, Vol. 55 ›› Issue (6) : 1039-1054.

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数学学报 ›› 2012, Vol. 55 ›› Issue (6) : 1039-1054. DOI: 10.12386/A2012sxxb0101
论文

由双Furstenberg族诱导的混沌

    吴新星, 朱培勇
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Chaos Via a Couple of Furstenberg Families

    Xin Xing WU, Pei Yong ZHU
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摘要

对于一对给定的Furstenberg族 F1F2, 定义稠 (F1,F2)-混沌, 稠 (F1,F2)-δ-混沌, 全局性 (F1,F2)-混沌, 全局性强 (F1,F2)-混沌和 (F1, F2)-敏感(以下将它们和 (F1, F2)-混沌统称为双Furstenberg族混沌), 得出了F-敏感和全局性(F1, F2)-混沌的一组等价刻画,还讨论了双Furstenberg族混沌在逆极限系统和乘积系统中的相关性质.

Abstract

For a couple of Furstenberg families F1 and F2, we introduce the notions of dense (F1,F2)-chaos, dense (F1,F2)-δ-chaos, general (F1,F2)-chaos, general strong (F1,F2)-chaos and (F1,F2)-sensitivity. Next, some equivalent conditions of F-sensitivity and general (F1,F2)-chaos are obtained. Finally, some properties of chaos via a couple of Furstenberg families in inverse limit systems and product systems are discussed.

关键词

Furstenberg族 / 混沌 / 敏感 / 逆极限系统 / 乘积系统

Key words

Furstenberg family / chaos / sensitivity / inverse limit system / product system

引用本文

导出引用
吴新星, 朱培勇. 由双Furstenberg族诱导的混沌. 数学学报, 2012, 55(6): 1039-1054 https://doi.org/10.12386/A2012sxxb0101
Xin Xing WU, Pei Yong ZHU. Chaos Via a Couple of Furstenberg Families. Acta Mathematica Sinica, Chinese Series, 2012, 55(6): 1039-1054 https://doi.org/10.12386/A2012sxxb0101

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基金

国家自然科学基金资助项目(10671134);四川省教育厅科研基金(12ZA098)
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