2015 Fiscal Year Final Research Report
Geometric analysis and dynamics on non-compact spaces
Project/Area Number |
25870334
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Geometry
Basic analysis
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Research Institution | Kyoto University |
Principal Investigator |
Tsukamoto Masaki 京都大学, 理学(系)研究科(研究院), 助教 (70527879)
|
Project Period (FY) |
2013-04-01 – 2016-03-31
|
Keywords | 力学系 / 幾何解析 / 信号処理 / 平均次元 / 正則曲線 / 位相的エントロピー |
Outline of Final Research Achievements |
Time-evolving systems are called dynamical systems. The number of freedom of dynamical systems per second is called mean dimension. We study this quantity mainly. First we develop a systematic method to calculate mean dimension of dynamical systems coming form geometry. As an application, we solved a problem which was posed by world-famous mathematician Gromov more than 10 years ago. We also study a foundational issues about mean dimension. A big success is the resolution of a problem which was posed by a Fields medalist Lindenstrauss more than 10 years ago. In the process of this success, we found an unexpected relation between signal processing (a kind of music or movie process) and dynamics.
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Free Research Field |
数学
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