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

Research Project

Project/Area Number 15H06128
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionKansai 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
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords可積分系 / 力学系 / 差分方程式 / 互いに素条件 / 離散力学系 / 解析学 / 数理物理 / 離散可積分系 / 代数的エントロピー / 特異点閉じ込め
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.

Report

(3 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Annual Research Report
  • Research Products

    (9 results)

All 2017 2016 2015

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 2 results) Presentation (5 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Journal Article] Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation2017

    • Author(s)
      Ryo Kamiya, Masataka Kanki, Takafumi Mase, Tetsuji Tokihiro
    • Journal Title

      Journal of Mathematical Physics

      Volume: 58 Issue: 1 Pages: 012702-012702

    • DOI

      10.1063/1.4973744

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singularity confinement and chaos in two-dimensional discrete systems2016

    • Author(s)
      Masataka Kanki, Takafumi Mase, Tetsuji Tokihiro
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 49 Issue: 23 Pages: 23LT01-23LT01

    • DOI

      10.1088/1751-8113/49/23/23lt01

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Graphs emerging from the solutions to the periodic discrete Toda equation over finite fields2016

    • Author(s)
      Masataka Kanki, Yuki Takahashi, Tetsuji Tokihiro
    • Journal Title

      NOLTA

      Volume: 7 Pages: 338-353

    • NAID

      130005161833

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic entropy of an extended Hietarinta-Viallet equation2015

    • Author(s)
      Masataka Kanki, Takafumi Mase and Tetsuji Tokihiro
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 48 Issue: 35 Pages: 355202-355202

    • DOI

      10.1088/1751-8113/48/35/355202

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Ultra-discrete Painleve equations2016

    • Author(s)
      Masataka Kanki
    • Organizer
      School - Abecedarian of SIDE
    • Place of Presentation
      モントリオール(カナダ)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 2次元離散戸田方程式の疑可積分拡張2016

    • Author(s)
      神谷亮、神吉雅崇、間瀬崇史、時弘哲治
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] 2次元離散戸田方程式の疑似可積分拡張2016

    • Author(s)
      神谷亮、神吉雅崇、間瀬崇史、時弘哲治
    • Organizer
      日本数学会年会
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] 拡張型Hietarinta-Viallet方程式の 代数的エントロピー2015

    • Author(s)
      神吉雅崇、時弘哲治、間瀬崇史
    • Organizer
      明治大学MIMS共同利用研究集会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-11-05
    • Related Report
      2015 Annual Research Report
  • [Presentation] 拡張型Hietarinta-Viallet方程式について2015

    • Author(s)
      神吉雅崇、時弘哲治、間瀬崇史
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      金沢大学
    • Year and Date
      2015-09-09
    • Related Report
      2015 Annual Research Report

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Published: 2015-08-26   Modified: 2018-03-22  

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