2014 Fiscal Year Final Research Report
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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| Keywords | 力学系 |
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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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| Free Research Field |
大域解析学・力学系
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