Complex dynamical systems and related C*-algebras
| Project/Area Number |
16K05178
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Okayama University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 自己相似写像 / 作用素環 / K- 群 / コア / トレース / イデアル / C*-環 / K-群 / 離散力学系 / シフト / 次元群 / 行列表現 / 有理関数力学系 / 複素力学系 / 極大可換環 / C*環 / ヒルベルト双加群 |
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| Outline of Final Research Achievements |
The results of this research projects are as follows. I defined dimension group of a self-similar map through the C*-algebra associated with the original self-similar map, and showed that this is a generalization of the case without branched points. As an example, I showed that the K_0 group of the core of the C*-algebra associated with the tent map is the ring of integer, and the canonical endomorphism is isomorphic to the shift of multiplicity 1, using the paring of discrete model traces and elements of K_0 group of the core.
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| Academic Significance and Societal Importance of the Research Achievements |
分岐点を持つ力学系からC*-環を構成する研究について、分岐点を付随するC*-環の定義に積極的に取り込んだ研究は他にあまり例がなく、力学系と作用素環の世界に及ぼす影響は非常に大きい。
特に、分岐点をもつ自己相似写像から生成される C*-環の代数不変量からもとの分岐点の情報を取り出す試みは、これまでほとんど行われていないので、作用素環と力学系の研究をつなぐ分野において、学術的な意義は大きい。
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Report
(8 results)
Research Products
(19 results)
