| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
We obtained a criterion to hold the large deviation principle for smooth dynamical systems on the interval. If a multimodal map without flat critical points has the following properties: (1) the exponential growth of the derivative on the set of critical values with respect to the time evolution; (2) the sub-exponential slow recurrence of the critical orbits; (3) the topological exactness, the large deviation principle of level 2 holds. From our result it is shown that almost every stochastic quadratic map satisfies the large deviation principle. Moreover we gave a representation of the Birkhoff spectrum by using thermodynamic formalism, and showed its continuity.
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