2010 Fiscal Year Final Research Report
Study on Complex dynamical systems and operator algebras
| Project/Area Number |
19340040
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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 | Kyushu University |
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Principal Investigator |
WATATANI Yasuo Kyushu University, 大学院・数理学研究院, 教授 (00175077)
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| Co-Investigator(Kenkyū-buntansha) |
KOSAKI Hideki 九州大学, 大学院・数理学研究院, 教授 (20186612)
MATSUI Taku 九州大学, 大学院・数理学研究院, 教授 (50199733)
KAJIWARA Tsuyoshi 岡山大学, 大学院・環境学研究科, 教授 (50169447)
UEDA Yoshimichi 九州大学, 大学院・数理学研究院, 准教授 (00314724)
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| Co-Investigator(Renkei-kenkyūsha) |
MASUDA Toshihiko 九州大学, 大学院・数理学研究院, 准教授 (60314978)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 作用素環 / 複素力学系 |
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| Research Abstract |
In the research we constructed C*-algebras of operators on Hilbert spaces for complex dynamical systems on a complex plane by the iteration of meromorphic functions like rational functions and transcendental entire functions. We found unexpected relations between complex dynamical systems and operator algebras. Self-similarity of Julia sets of complex dynamical systems corresponds to purely infinite simplicity of the associated C*-algebras. The branch structure of complex dynamical systems is related with the structure of KMS states (equilibrium states) for the gauge actions on the associated C*-algebras. We showed that we can recover the degree of the rational function, the number of branched points and the number of exceptional points.
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