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Mathematical Sciences: Multiple Recurrence Nonconventional Ergodic Averages Wiener-Wintner Return Times Theorems

Mathematical Sciences: Multiple Recurrence Nonconventional Ergodic Averages Wiener-Wintner Return Times Theorems
数学科学:多重递归非常规遍历平均维纳-温特纳返回时间定理
批准号:
9305754
负责人:
Idris Assani
金额:
$5.25万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
1993
资助国家:
美国
项目状态:
已结题
起止时间:
1993-05-01 至 1996-10-31

项目摘要

项目成果

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中文摘要
翻译
阿萨尼将调查多次复发的问题, Furstenberg提出的非常规平均数。 他将 研究了这些非常规算法点态收敛性和范数收敛性 平均值。 他将研究维纳-温特纳版本的回归 Furstenberg在他的证明中使用了 Szemeredi的算术级数定理。 该项目涉及遍历理论的研究。 遍历 理论一般涉及理解的平均行为, 系统的动力学过于复杂或混乱, 在微观细节上进行跟踪。 在“动态”标题下, 现代理论认为, 变换作用于光滑空间。 这样遍历理论 与几何学接触,以寻求对 齐性空间
英文摘要
Assani will investigate problems of multiple recurrence and nonconventional averages introduced by Furstenberg. He will study pointwise and norm convergence of these non-conventional averages. He will study the Wiener-Wintner versions of return times theorem which were used by Furstenberg in his proof of Szemeredi's theorem on arithmetic progressions. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.
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会议论文
Ergodic Theory and Dynamical Systems Workshops
Ergodic Theory and Dynamical Systems Workshop
Ergodic Theory and Dynamical Systems Workshop
Ergodic Theory and Dynamical Systems Workshop
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences