| Budget Amount *help |
¥16,510,000 (Direct Cost: ¥12,700,000、Indirect Cost: ¥3,810,000)
Fiscal Year 2013: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
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| Outline of Final Research Achievements |
We studied the bifurcation of chaotic dynamical systems, especially low dimensional complex dynamical systems. In order to study the bifurcation of parabolic or semi-parabolic fixed points, we established the theory of parabolic and near-parabolic renormalization, and found an invariant space of functions under these renormalizations. We introduced the notion of dynamical charts, and combining the invariant space of near-parabolic renormalization, we studied the dynamical properties and invariant sets (called hedgehogs) near irrationally invariant fixed points. We also studied the local structure and the bifurcation of semi-parabolic fixed point of two-dimensional holomorphic mappings, and obtained results on the continuity and discontinuity of the parabolic/attracting basins and unstable manifolds.
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