| Project/Area Number |
24654029
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ryukoku University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
OKA Hiroe (KOKUBU Hiroe) 龍谷大学, 理工学部, 教授 (20215221)
ITO Toshikazu 龍谷大学, 経済学部, 教授 (60110178)
TSUJIKAMI Tetsuya 龍谷大学, 理工学部, 教授 (80243179)
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| Research Collaborator |
HIZUME Akio
SUSHIDA Takamichi (00751158)
SCARDUA Bruno
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 螺旋葉序 / 連分数 / タイリング / 複素葉層構造 / 折り紙 / モース指数 |
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| Outline of Final Research Achievements |
Our main results are on the global structure of spiral tilings with similarity symmetry, and on the transversality of holomorphic foliations with spheres, having the symmetry of complex conjugacy. The parameter space of quadrilateral Voronoi spiral tilings is written as a family of real algebraic curves, which is related to the continued fraction expansion of the divergence angle. The limit set of the shapes of tiles also relates to the continued fraction expansion. As an application of phyllotactic geometry, we propose phyllotactic configurations of seats in a colosseum.
The transversality of holomorphic foliations with spheres is studied from the viewpoint of a complex-conjugate dynamical system. In a good condition, the variety of contact is a real two-dimensional manifold.
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