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周期倍分岐理論の新展開：モノドロミーの観点から
About This Project
- Japan Grant Number
- JP25K00919 (JGN)
- Funding Program
- Grants-in-Aid for Scientific Research
- Funding Organization
- Japan Society for the Promotion of Science
Kakenhi Information
- Project/Area Number
- 25K00919
- Research Category
- Grant-in-Aid for Scientific Research (B)
- Allocation Type
-
- Multi-year Fund
- Review Section / Research Field
-
- Basic Section 12040:Applied mathematics and statistics-related
- Basic Section 12030:Basic mathematics-related
- Sections That Are Subject to Joint Review: Basic Section12030:Basic mathematics-related , Basic Section12040:Applied mathematics and statistics-related
- Research Institution
-
- Institute of Science Tokyo
- Project Period (FY)
- 2025-04-01 〜 2030-03-31
- Project Status
- Granted
- Budget Amount*help
- 18,850,000 Yen (Direct Cost: 14,500,000 Yen Indirect Cost: 4,350,000 Yen)
Research Abstract
本研究では，周期倍分岐がなぜカオスの発生で本質的なのかを明かにし，またそれをカオスの予測・制御に活用するため，(A)複数パラメータ系における周期倍分岐カスケードの生成・消滅を記述する理論を構築し，(B)周期が2倍される理由を実力学系の隠れた対称性に基づいて解明し，(C)得られた理論を用いてカオス発生位置の予測と制御を行うことを目指す．特に、申請者が開発したモノドロミー理論を拡張し，カオス発生に関与する代数的条件や同変ホモロジー理論を用いることで，周期倍分岐の本質理解と複雑なパラメータ空間におけるアルゴリズムの開発を目指す．
Details 詳細情報について
-
- CRID
- 1040585407823599360
-
- Text Lang
- ja
-
- Data Source
-
- KAKEN