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Applications of entropy compression algorithms to dynamical systems and fluid mechanics

Research Project

Project/Area Number 15K04986
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionChubu University (2017)
Hokkaido University (2015-2016)

Principal Investigator

ARAI Zin  中部大学, 創発学術院, 教授 (80362432)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords力学系 / アルゴリズム / 数値解析 / 数理モデル / 数値解析・数理モデル
Outline of Final Research Achievements

Using recent information theoretic methods such as the succinct data structure, we have developed some algorithms for improving the computational capability of graph theoretical methods in dynamical systems and fluid mechanics. These algorithms enable us to use compressed and memory-efficient data structures for computing the structure of the invariant sets of dynamical systems so that we can handle more practical and higher dimensional problems.
We also studied the relation between the information theoretic invariants and topological invariants of the system. In particular, we have shown that, for some dynamical systems, there is an explicit relation between the information theoretic entropy of the data required for the graph representation of the system and the topological entropy of the system.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (17 results)

All 2018 2017 2016 2015 Other

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (13 results) (of which Int'l Joint Research: 6 results,  Invited: 6 results) Remarks (2 results)

  • [Journal Article] On parameter loci of the Henon family2018

    • Author(s)
      Zin Arai and Yutaka Ishii
    • Journal Title

      Communications in Mathematical Physics

      Volume: 印刷中

    • NAID

      120006940730

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On loops in the hyperbolic locus of the complex Henon map and their monodromies2016

    • Author(s)
      Zin Arai
    • Journal Title

      Physica D

      Volume: 印刷中

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] The Conley index for real and complex Henon maps2017

    • Author(s)
      Zin Arai
    • Organizer
      力学系 ー 理論と応用の連携探索
    • Related Report
      2017 Annual Research Report
  • [Presentation] On computation of the monodromy of the Henon map and its applications2017

    • Author(s)
      Zin Arai
    • Organizer
      Foundations of Computational Mathematics 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 複素からみた分岐理論2017

    • Author(s)
      荒井迅
    • Organizer
      Interaction between Pure and Applied Mathematics 2017
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] The Conley index for real and complex dynamical systems2017

    • Author(s)
      Zin Arai
    • Organizer
      冬の力学系研究集会
    • Place of Presentation
      日本大学軽井沢研修所(長野県・軽井沢市)
    • Related Report
      2016 Research-status Report
  • [Presentation] 複素エノン写像に対する計算機援用証明について2016

    • Author(s)
      荒井迅
    • Organizer
      力学系と計算
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2016-03-24
    • Related Report
      2015 Research-status Report
  • [Presentation] On rigorous verification of the crossed mapping condition2016

    • Author(s)
      Zin Arai
    • Organizer
      Computation in Dynamics
    • Place of Presentation
      プロビデンス(アメリカ合衆国)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] An introduction to topological data analysis2016

    • Author(s)
      Zin Arai
    • Organizer
      4th international symposium on ALP
    • Place of Presentation
      北海道大学(北海道・札幌市)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 複素から見た分岐理論2016

    • Author(s)
      荒井迅
    • Organizer
      芝浦数理談話会
    • Place of Presentation
      芝浦工業大学(埼玉県・さいたま市)
    • Related Report
      2016 Research-status Report
  • [Presentation] On topological tools for network analysis2016

    • Author(s)
      Zin Arai
    • Organizer
      情報セキュリティにおける数学的方法とその実践
    • Place of Presentation
      北海道大学(北海道・札幌市)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On combinatorial methods for dynamical systems and fluid mechanics2015

    • Author(s)
      Zin Arai
    • Organizer
      16th RIES-Hokudai International Symposium
    • Place of Presentation
      ガトーキングダムサッポロ(北海道札幌市)
    • Year and Date
      2015-11-10
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 複素力学系のモノドロミー2015

    • Author(s)
      荒井迅
    • Organizer
      解析学の耳袋
    • Place of Presentation
      プラザヴェルデ(静岡県沼津市)
    • Year and Date
      2015-10-28
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 力学系的・組合せ的な手法による流れの分解について2015

    • Author(s)
      荒井迅
    • Organizer
      流体力学系年会
    • Place of Presentation
      東京工業大学(東京都目黒区)
    • Year and Date
      2015-09-26
    • Related Report
      2015 Research-status Report
  • [Presentation] Rigorous Verification of the crossed mapping condition for holomorphic dynamical systems2015

    • Author(s)
      Zin Arai
    • Organizer
      Theory and Practice of Real Computation
    • Place of Presentation
      明治大学(東京都千代田区)
    • Year and Date
      2015-07-12
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Remarks] Web page of Zin Arai

    • URL

      http://www.isc.chubu.ac.jp/zin_arai/

    • Related Report
      2017 Annual Research Report
  • [Remarks] Web page of Zin ARAI

    • URL

      http://www.math.sci.hokudai.ac.jp/~zin/

    • Related Report
      2016 Research-status Report 2015 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2019-03-29  

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