| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
The purpose of this study is to clarify various properties of discrete dynamical systems through actions on the geometric structure of phase spaces. As a concrete result, we found a general formula for constructing bi-rational maps from abstract actions on Picard groups, and established a method of deautonomization that preserves integrable structures. We also established a method for constructing a phase space (initial value space) in which the action is appropriately represented for higher dimensional dynamical systems. For higher dimensional dynamical systems that are not integrable, we found a way to construct algebraically stable manifolds. Furthermore, we proposed a natural solution construction method for the Quispel-Roberts-Thompson map, which is a self-isomorphic map of elliptic surfaces.
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