| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
The purpose of this project to to study mean dimension. Mean dimension is the number of degrees of freedom per unit time for describing dynamical systems. We found the ``double variational principle for mean dimension''. Given a minimal dynamical system, we proved that its mean dimension is equal to the minimax value of the rate distortion dimension (the quantity in information theory). This discovery opens a very new interaction between dynamical systems theory and information theory.
We also found several interesting things around mean dimension. In particular, we solved a problem about ``marker property'', which asks whether there is a free dynamical system violating the marker property.
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