Thermodynamic formalism for the Henon map at the first bifurcation
| Project/Area Number |
23740121
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Keio University (2013-2014)
Kyoto University (2012)
The University of Tokyo (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 力学系 / エノン写像 / 国際研究者交流 / 韓国 / 双曲性 / 分岐 / エルゴード理論 / 国際情報交換 / アメリカ / 熱力学形式 |
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| Outline of Final Research Achievements |
We investigated the dynamics of the Henon map at the first bifurcation parameter with the use of themodynamic fomalism, and proved the existence and uniqueness of equilibrium measures. We also derived a version of Bowen-Manning formula which connects the Hausdorff dimension of the invariant set with the entropy and Lyapunov exponent of invariant measures. We also proved nice statistical properties of equilibrium measures, such as an exponential decay of correlations and the central limit theorem.
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Report
(5 results)
Research Products
(17 results)
