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Analytic study of Painleve equations and a nelated clans of equation

Research Project

Project/Area Number 17340050
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKeio University

Principal Investigator

SHIMOMURA Shun  Keio University, Facualry of Science and Technlogy, Prof. (00154328)

Co-Investigator(Kenkyū-buntansha) TANI Atusi  Keio University, Faculty of Science and Technology, Prof (90118969)
SHIOKAWA Iekata  Keio University, Faculty of Science and Technology, Honorary Prof (00015835)
KIMURA Hironobu  Kumamoto University, Faculty of Science and Technology, Professor (40161575)
HANAOKA Yoshishige  Kumamoto University, Faculty of Science and Technology, Professor (30208665)
ISHIGAKI Katsuya  Nippon Insitute of Technology, Faculty of Engineering, Associate Professor (60202991)
菊池 紀夫  慶應義塾大学, 理工学部, 教授 (80090041)
藤解 和也  金沢大学, 大学院・自然科学研究科, 助教授 (30260558)
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥5,050,000 (Direct Cost: ¥4,600,000、Indirect Cost: ¥450,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2006: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2005: ¥1,600,000 (Direct Cost: ¥1,600,000)
KeywordsPainleve equations / Ganier system / quasi-Painleve property / Fibonacci numbers / Painleve方程式 / Garnier系 / 準Painleve性 / 特異点 / Painleve equation / 準パンルヴェ性
Research Abstract

1. We found a class of nonlinear ordinary differential equations containing the first Painleve equation such that each equation admits the quasi-Painleve property, and discussed the global multi-valuedness of their solutions. We also found a similar clean of equations containing the second Painleve equation.
2. For solutions of the fifth Painleve equation, we examined value distribution in a sectonial domain. Under a certain condition, we proved the equi-distribution of values.
3. For a degenerate Garnier system corresponding to the first Painleve equation, we obtain an asymptotic solution around a singular locus.
4. We examined algebraic independence and algebraic relations for reciprocal rums of Fibonacci numbers. We also discussed their relation to zeta values.

Report

(4 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (24 results)

All 2008 2007 2006 2005 Other

All Journal Article (21 results) (of which Peer Reviewed: 6 results) Presentation (3 results)

  • [Journal Article] A Class of diffecestial equationd of PI-type toith the guasi-painleup propcity2007

    • Author(s)
      Shun Shimomura
    • Journal Title

      Aun.Mat.Pusa Appl 186

      Pages: 267-280

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Aiymptotic solntions of a degeneiate Gasnies oystem of the finst Poai leve type2007

    • Author(s)
      Shun Shimomura
    • Journal Title

      RIMS Kokyuroku Beisatsu B2

      Pages: 227-237

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Algelraic nelationg for reciprocal rums of Fibonacci numbeis2007

    • Author(s)
      Caisten Elsnes, Shun Shimomura Iehata Seriokawa
    • Journal Title

      Acta Arith 130

      Pages: 37-60

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] A class of differential equations of PI-type with the quasi-Painleve property2007

    • Author(s)
      Shun, Shimomura
    • Journal Title

      Ann. Mat. Pma Appl 186

      Pages: 267-280

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Asymptotic solutions of a degemenate Gannier system of the tinst Painleve type2007

    • Author(s)
      Shun, Shimomura
    • Journal Title

      RIMS Kokyuroku Bessatsu B2

      Pages: 227-237

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Algelraic nelations for recipnocal rums of Fibonacci numbers2007

    • Author(s)
      Cansten Elsner, Shun Shimomura, Iekata Shiokawa
    • Journal Title

      Acta Arith 130

      Pages: 37-60

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] A lass of diffenertial equations of PI-type with the quasi-Painleve property2007

    • Author(s)
      Shun Shimomura
    • Journal Title

      Ann.Mat.Pura Appl 186

      Pages: 267-280

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptoric solutions of a degenerate Garnier system of the first Painleve type2007

    • Author(s)
      Shun Shimomura
    • Journal Title

      RIMS Kokyuroku Bessatsu B2

      Pages: 227-237

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic relations for neciprocal sums of Fibonacci numbers2007

    • Author(s)
      Carster Elsner, Shun Shimomura Iekata Shiokawa
    • Journal Title

      Acta Arith 130

      Pages: 37-60

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A closs of fifperential equations of PI-type with the quasi-Painleaie property2007

    • Author(s)
      Shun Shimomura
    • Journal Title

      Ann. Mat. Pura Appl. 186

      Pages: 267-280

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A family of sohting of a hither onder PVI eyuation near a regular singulaity2006

    • Author(s)
      Shun Shimomura
    • Journal Title

      J. Physics A 39

      Pages: 12153-1216

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Algehaic nelations for reciprocal sums of binary recurrences2006

    • Author(s)
      Carsten Elsmer, Shun Shimomura, Iehata shiokawa
    • Journal Title

      Seminar on Mathematical Sciences, Diophanting Ancly513 and Related Fiedds 2006 35

      Pages: 77-92

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On confluences of general hypergeunetic systems2006

    • Author(s)
      Hironobu Kimura, Kyoichi Takano
    • Journal Title

      Tohoku Math. J. 58

      Pages: 1-31

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Construction of rigid local sgstens and integral representatims of their sections2006

    • Author(s)
      Yoshihige Haraoka, Toshiaki Yokoyama
    • Journal Title

      Math. Nachr. 279

      Pages: 255-271

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Singular direcrins of meromenglic sohtions of osml nonoutonomons Schroder yguahbns2006

    • Author(s)
      Katsuya Ishizaki, Niro Yanagihara
    • Journal Title

      Adv. Stud. Pure Math. Potential throng in Matsue 44

      Pages: 155-166

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Meromorphic solutions of a Riccati differential equation with a doubly periodic coefficient2005

    • Author(s)
      Shun Shimomura
    • Journal Title

      J.Math.Anal.Appl. 304

      Pages: 644-651

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On certain nonlinear differential equation2005

    • Author(s)
      Shun Shimomura
    • Journal Title

      Proceedings of the 12th International Conference on Finite on Infinite Dimensional Complex Analysis and Applications

      Pages: 299-304

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On the twisted de Rahm cohomology group of the general hypergeometric integral of type (q+1, 1^<N-q>)2005

    • Author(s)
      Hironobu Kimura
    • Journal Title

      J.Math.Sci.Univ.Tokyo 12

      Pages: 165-189

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Cohomological intersection numbers for the generalized Airy functions at Veronese points2005

    • Author(s)
      I.Basalaeva, H.Kimura, T.Nakazuka
    • Journal Title

      Funkcial.Ekvac. 48

      Pages: 161-181

    • NAID

      130000141284

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Borel and Julia directions of meromorplic Schroder functions2005

    • Author(s)
      Katsuya Ishizaki, Niro Yanagihara
    • Journal Title

      Math.Proc. Cambridge Phil.Soc. 139

      Pages: 139-147

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A class of differential equation of PI-type with the quasi-Painle' property

    • Author(s)
      Shun Shimomura
    • Journal Title

      Ann.Mat.Pura Appl. (to appear)

    • Related Report
      2005 Annual Research Report
  • [Presentation] 角領域における値分布論とその応用2008

    • Author(s)
      下村 俊
    • Organizer
      日本数学会(函数論分科会特別講演)
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Shun, Shimomura2008

    • Author(s)
      Shun, Shimomura
    • Organizer
      Annual Mectiny The Mathematical Society of Japan
    • Place of Presentation
      Kinki University
    • Year and Date
      2008-03-24
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 角領域における値分布論とその応用2008

    • Author(s)
      下村 俊
    • Organizer
      日本数学会年会(函数論分科会特別講室)
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2007 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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