2005 Fiscal Year Final Research Report Summary
Study of ergodic properties of partially hyperbolic dynamical systems
| Project/Area Number |
14340052
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
TSUJII Masato Hokkaido Univ., Grad.School of Sci., Asso.Prof., 大学院・理学研究科, 助教授 (20251598)
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| Co-Investigator(Kenkyū-buntansha) |
ASAOKA Masayuki Kyoto Univ., Grad.School of Sci., Lecturer, 大学院・理学研究科, 講師 (10314832)
KOKUBU Hiroshi Kyoto Univ., Grad.School of Sci., Asso.Prof., 大学院・理学研究科, 助教授 (50202057)
SHISHIKURA Mitsuhiro Kyoto Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (70192606)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Dynamical system / Ergodic theory / Chaos / Partially hyperbolic dynamics |
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| Research Abstract |
In this study, we investigate ergodic properties of partially hyperbolic dynamicals systems. As one of the main results, we showed that generic partially hyperbolic endomorphism one two dimensional manifolds has finitely many physical measures (invariant measure that has attracting nature) such that the distribution of the orbits for almost every initial points with respect to the Lebesgue measure is asymptotic to one of those measures. Since this kind of results has only known for uniformly hyperbolic dynamical systems and one dimensional dynamical systems, this result is a kind of break-through. As a closely related subject, we also studied applications of functional analytic method in dynamical sytems. As a main result in this direction, we contructed a Banach spaces of distributions on which the Ruelle transfer operators acts on naturally and the essential spectral radius of that action is shown to be small. This lead to many results on decay of correlations and study of dynamical zeta functions.
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