Discrete and Ultradiscrete integrable systems in terms of the theory of number theoretic dynamical systems

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K14211
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kansai University
• Principal Investigator: KANKI Masataka 関西大学, システム理工学部, 准教授 (20755897)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 可積分系 / 漸化式 / 超離散系 / 力学系

Outline of Final Research Achievements

The aim of this research is to rigorously re-define the integrability of discrete dynamical systems through the study of the algebraic and the number theoretic aspects of difference equations.
An elaboration on the integrability criteria helps us to define the "integrability" of multi-dimensional lattice systems and the systems defined over a number theoretic field. We have defined several new types of difference equations, which are considered to be "partially" integrable in terms of our integrability criterion called the "co-primeness" condition.
We expect that this study leads us to a novel perspective in the field of integrable systems and mathematical physics.

Free Research Field

大域解析学

Academic Significance and Societal Importance of the Research Achievements

可積分系の研究には長い歴史があるが、離散系における可積分性についての厳密な取り扱いは発展途上である。本研究はこのテーマについて、従来の方程式を拡張した系に適応できる新しい可積分性判定基準として「互いに素条件」を導入した。
またこれらの基準の意味するところを、既知の判定基準と比較検討することで一見単純に思えるが難しい漸化式の世界の複雑さを解き明かすための準備となる研究を行うことができた。