Study on cellular automata derived from discrete integrable systems
| Project/Area Number |
26400109
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
|
|---|
| Research Collaborator |
KANKI Masataka
MASE Takafumi
KAMIYA Ryo
|
|---|
| Project Period (FY) |
2014-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 準可積分系 / co-primeness条件 / 特異点閉じ込め / Laurent性 / 代数的エントロピー / 超離散 / 超離散系 / coprimeness / LP代数 / 離散可積分系 / 離散戸田方程式 / 線形化可能系 / co-primeness / 戸田格子方程式 / 特異値閉じ込め / 離散KdV方程式 / Hietarinta-Viallet方程式 / 得意点閉じ込め |
|---|
| Outline of Final Research Achievements |
We reformulated the singularity confinement property as the co-primeness property of the discrete mappings. Typical discrete integrable systems including higher dimensional discrete soliton equations are proved to satisfy this co-primeness property. We proposed the notion of the discrete quasi-integrable equation which has the co-primeness property but is not integrable such as the Hietarinta-Viallet equation. Higher dimensional analogue of the Hietarinta-Viallet equation and quasi-integrable analogue of the discrete Toda lattice equation and its hegher dimensional extensions were constructed. We also investigated their mathematical structure by showing the Laurent property of the lower dimensional equations reduced from the quasi-integrable quations and by rigorously estimating their algebraic entropy.
|
| Academic Significance and Societal Importance of the Research Achievements |
特異点閉じ込めは，坂井によって，特異点解消による双有理写像の構成として幾何学的に説明された．本研究は，この特異点閉じ込めを代数的に再定式化したものであり，学術的な意義は大きい．実際に，この定式化によって，新たに離散準可積分系と呼ばれるよい数理構造をもつ力学系のクラスを定式化でき，多くのよい数学的性質を持ちながら可積分ではない系を特徴づけることができた．今後は，この離散準可積分系の分類問題に取り組まなければならないが，そのための数学的な準備や手法の開発は，当該数理科学分野において大きな意味を持つと思われる．
|
Report
(6 results)
Research Products
(16 results)
