| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| 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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