| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
I mainly studied discrete dynamical systems defined on low-dimensional lattices and developed methods for deciding on the integrability or non-integrability of such discrete systems. In particular, I classified the types of singularities that may arise in mappings of the complex projective plane and proposed several new methods for deciding on the integrability of such mappings, based on the structure of their singularities. I also developed a systematic method for constructing discrete Painleve equations ― the prototypical discrete integrable system ― based on the symmetries and geometric structure of integrable birational maps.
Furthermore, using certain algebraic and combinatorial properties of ultradiscrete systems, I discovered new solution methods for two types of soliton cellular automata.
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