| Budget Amount *help |
¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2020: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2019: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2018: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Outline of Final Research Achievements |
We have developed a mathematical framework for visualizing and realizing quantum chemical reaction networks. Following our recent work to reduce a dimension of a set of reference structures along the intrinsic reaction coordinate by a classical multidimensional scaling approach, we proposed the method to project on-the-fly trajectories into a reduced-dimension subspace determined by the network. By extending the equivariant Morse theory, we have also developed an equivariant version of the Conley index theory for dynamical systems with a group action. It is then applied to the study of complex dynamical systems and used to prove the topological properties of the Julia set of the quadratic map and the Henon map.
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