Dynamics of complex Henon maps: from dynamical space to parameter space
| Project/Area Number |
25287020
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
Ishii Yutaka 九州大学, 数理学研究院, 准教授 (20304727)
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| Co-Investigator(Kenkyū-buntansha) |
浅岡 正幸 京都大学, 理学研究科, 准教授 (10314832)
荒井 迅 中部大学, 創発学術院, 教授 (80362432)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥9,100,000 (Direct Cost: ¥7,000,000、Indirect Cost: ¥2,100,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
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| Keywords | ヘノン写像 / ジュリア集合 / ホースシュー / 反復写像系 / Henon 写像 / 精度保証計算 / マンデルブロー集合 / 複素ヘノン写像 / モノドロミー作用 / 双曲的ホースシュー / Hubbard tree / エノン写像 / ホースシュー領域 / 複素力学系 / 変分原理 / Julia 集合 / homotopy kernel / ハバード木 / 反復モノドロミー群 |
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| Outline of Final Research Achievements |
We obtained some results concerning combinatorial and topological aspects of both real and complex Henon maps. Among others, we studied topological properties of the hyperbolic horseshoe locus and the maximal entropy locus in the parameter space of the real Henon family, variational characterization of some invariant measures of the Henon maps at the boundary of the horseshoe locus, and the representation of the monodromy group action of the horseshoe locus for the complex Henon family to the automorphism group of the corresponding symbolic dynamics.
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Report
(6 results)
Research Products
(11 results)
