| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We studied classical and quantum dynamics in mixed Hamiltonian systems and obtained the following results: (1) we have rigorously proved the existence of infinity many stability islands for a certain piecewise linear map with hierarchical phase space by introducing a proper symbolic dynamics. (2) we have numerically observed the stable and unstable manifolds for the complex Henon map and found that the orbits are ergodic even though the dynamics in the real plane has mixed phase space, which serves as a semiclassical interpretation for the so-called amphibious eigenfunctions. (3) we have analyzed the Stokes geometry of quantum Henon map satisfying the horseshoe condition based on recent progress of the exact WKB analysis, and found that nontrivial cancellation of saddle points solutions takes places, reflecting the global nature of Stokes geometry.
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