Construction of the integrability criteria for discrete dynamical systems in view of their algebraic structures

2016 Fiscal Year Final Research Report

• Project/Area Number: 15H06128
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kansai University (2016); The University of Tokyo (2015)
• Principal Investigator: Kanki Masataka 関西大学, システム理工学部, 助教 (20755897)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Keywords: 可積分系 / 力学系 / 差分方程式 / 互いに素条件 / 離散力学系

Outline of Final Research Achievements

We have costructed one of the integrability criteria for discrete dynamical systems, by investigating the algebraic structures of the equations in detail.
We call this criterion the coprimeness condition, and have applied the criterion to many of the known integrable discrete dynamical systems.
We have constructed new types of 'quasi-integrable' equations, by our method of coprimeness-preserving extensions of the already known integrable and non-integrable equations. By introducing several parameters in the terms of the discrete KdV equation and the discrete Toda equation, we have obtained coprimeness-preserving and non-integrable (in the sense that the degrees of their iterates grow exponentially) extension of these discrete equations.

Free Research Field

解析学基礎