| Project/Area Number |
15K04943
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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 | 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群) |
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Principal Investigator |
Fujimura Masayo 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群), 総合教育学群, 准教授 (00531758)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 有理関数 / 関数論 / 数式処理 / 解析学 / ブラシュケ積 / 複素力学系 |
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| Outline of Final Research Achievements |
Every point in the moduli space of rational maps of degree d contains an element in so-called "normalized family" as a represantative. Using this normalized family, I studied the type of degeneration of rational maps.
I also studied the geometry of Blaschke products. The interior curve of Blaschke product is defined by an envelope and the defining equation is not simple. I introduced the exterior curve of Blaschke product of degree d and proved the curve was an algebraic curve of degree at most d-1. Moreover, I succeeded in finding there was a duality-like relationship between the interior and exterior curves of Blaschke product. This provides a way to analyze the interior curve by using the exterior curve.
I also collaborated with foreign researchers on the problem of triangular ratio metric.
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| Academic Significance and Societal Importance of the Research Achievements |
ブラシュケ積の幾何学的性質に関しては、行列の数域などと関連があり他分野への応用が多い内部曲線についての研究が多くなされているが、次数が高い場合は内部曲線の定義方程式を求めることは難しかった。本研究で導入した外部曲線と内部曲線との関係がわかったことで、比較的解析が容易な外部曲線を経て内部曲線の性質を調べることが可能になった。研究には数式処理システムを利用しているが、その研究手法の応用などが期待され海外の研究者らとの共同研究にも着手することができた。
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