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Study of structures of singular phenomena via complex global analysis

Research Project

Project/Area Number 23540207
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionHiroshima University

Principal Investigator

YOSHINO Masafumi  広島大学, 理学(系)研究科(研究院), 教授 (00145658)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsハミルトン系 / 非可積分性 / モノドロミー / ボレル総和法 / モーメント総話法 / 特異摂動 / 完全漸近解析 / 超幾何方程式系 / モーメントボレル総和法 / 接続問題 / 超幾何方程式 / モーメント総和法 / 接続係数 / 不確定特異点
Research Abstract

We have obtained the concrete formula of the monodromy of a certain confluent hypergeometric system which can be written in a Hamiltonian form. The method may be extended to more general system of equations and may be applied to the study of connection formulas near the irregular singular point. The method has some similarity to the so-called KAM theory.
The other result of the research is the proof of the Borel summability of a singular perturbative formal solution of a certain a multi-dimensional Fuchsian equation. This results was proved in the case of one variable. Using the method in the above we have analyzed the analytic behavior of Lotoka Volterra system of three species with evolutional effect.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (28 results)

All 2013 2012 2011 Other

All Journal Article (13 results) (of which Peer Reviewed: 13 results) Presentation (11 results) (of which Invited: 3 results) Remarks (4 results)

  • [Journal Article] Global Properties of Evolutional Lotka-Volterra System2013

    • Author(s)
      吉野正史, 田中 嘉成
    • Journal Title

      Advances in Pure Mathematics

      Volume: Vol.3 , No.9 Issue: 09 Pages: 709-718

    • DOI

      10.4236/apm.2013.39097

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Smooth-integrable and analytic-nonintegrable resonant Hamiltonians2013

    • Author(s)
      吉野正史
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: Vol.40(ISSN 1881-6193) Pages: 177-189

    • URL

      http://www.kurims.kyoto-u.ac.jp

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic analysis to Goursat problems2013

    • Author(s)
      吉野正史
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: Vol.37(ISSN 1881-6193) Pages: 247-262

    • URL

      http://www.kurims.kyoto-u.ac.jp

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic analysis to Goursat problems2013

    • Author(s)
      Masafumi Yoshino
    • Journal Title

      RIMS Kokyuuroku Bessatsu

      Volume: 37 Pages: 247-262

    • Related Report
      2013 Annual Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Smooth-integrable and analytic- nonintegrable resonant Hamiltonians2013

    • Author(s)
      Masafumi Yoshino
    • Journal Title

      RIMS Kokyuuroku Bessatsu

      Volume: 40 Pages: 177-189

    • Related Report
      2013 Annual Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Analytic- nonintegrable resonant Hamiltonians which are integrable in a sector2012

    • Author(s)
      吉野正史
    • Journal Title

      Proceedings of the 19th ICFIDCAA Hiroshima 2011, Tohoku University Press

      Volume: (ISBN 978-4-86163-219-8) Pages: 85-96

    • URL

      http://www.tups.jp

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Summability of first integrals of a C ω -nonintegrable resonant Hamiltonian system2012

    • Author(s)
      吉野正史
    • Journal Title

      Banach Center Publ

      Volume: Vol. 97 Pages: 169-178

    • DOI

      10.4064/bc97-0-13

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sectorial solution to semilinear singular partial differential equation2012

    • Author(s)
      吉野正史
    • Journal Title

      manuscripta math

      Volume: Vol.137 Issue: 3-4 Pages: 441-455

    • DOI

      10.1007/s00229-011-0474-5

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Summability of first integrals of a C^ω-nonintegrable resonant Hamiltonian system2012

    • Author(s)
      Masafumi Yoshino
    • Journal Title

      Publication in Banach Center Publ.

      Volume: 97 Pages: 169-178

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Analytic- nonintegrable resonant Hamiltonians which are integrable in a sector2012

    • Author(s)
      Masafumi Yoshino
    • Journal Title

      Proceedings of the 19th ICFIDCAA Hiroshima 2011, Tohoku University Press

      Volume: 1 Pages: 85-96

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic property of divergent formal solutions in linearization of singular vector field2011

    • Author(s)
      吉野正史
    • Journal Title

      Publications in RIMS

      Volume: Vol.47 No.4

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Werner Balser , Integrability of Hamiltonian systems and transseries expansions2011

    • Author(s)
      吉野正史
    • Journal Title

      Math. Z

      Volume: Vol.268 Issue: 1-2 Pages: 257-280

    • DOI

      10.1007/s00209-010-0669-6

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic property of divergent formal solutions in linearization of singular vector field2011

    • Author(s)
      Masafumi Yoshino
    • Journal Title

      Publ. RIMS Kyoto Univ.

      Volume: 47 Pages: 937-958

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Stokes geometry and summability in the linearization problem for a singular vector field2013

    • Author(s)
      吉野正史
    • Organizer
      Global study of differential equations in the complex domain
    • Place of Presentation
      Warsaw( Poland)
    • Year and Date
      2013-09-06
    • Related Report
      2013 Final Research Report
  • [Presentation] Singular perturbative analysis of Poincare's theorem for a singular vector field2013

    • Author(s)
      吉野正史
    • Organizer
      Formal and Analytic Solutions of Differential and Difference Equations
    • Place of Presentation
      Warwaw (Poland)
    • Year and Date
      2013-08-30
    • Related Report
      2013 Final Research Report
  • [Presentation] Monodromy property of analytic non integrable Hamiltonian system2013

    • Author(s)
      Masafumi Yoshino
    • Organizer
      Banach center, Poland
    • Place of Presentation
      Bedlewo (Poland)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Singular perturbative analysis of Poincar\'e's theorem for a singular vector field2013

    • Author(s)
      Masafumi Yoshino
    • Organizer
      Banach center, Poland
    • Place of Presentation
      Warsaw (Poland)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 非可積分なハミルトン系の接続問題2012

    • Author(s)
      吉野正史
    • Organizer
      日本数学会関数方程式分科会総合的研究
    • Place of Presentation
      東大
    • Year and Date
      2012-12-15
    • Related Report
      2013 Final Research Report
  • [Presentation] 非可積分なハミルトン系の接続問題2012

    • Author(s)
      吉野正史
    • Organizer
      日本数学会関数方程式分科会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] あるハミルトン系の接続問題について2012

    • Author(s)
      吉野正史
    • Organizer
      日本数学会関数方程式分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Monodromy property of analytic non integrable Hamiltonian system2011

    • Author(s)
      吉野正史
    • Organizer
      The 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      Hiroshima (Japan)
    • Year and Date
      2011-12-14
    • Related Report
      2013 Final Research Report
  • [Presentation] Summability of first integrals of a resonant Hamiltonian system2011

    • Author(s)
      吉野正史
    • Organizer
      Formal and Analytic Solutions of Differential and Difference Equations
    • Place of Presentation
      Bedlewo (Poland)
    • Year and Date
      2011-08-10
    • Related Report
      2013 Final Research Report
  • [Presentation] Summability of first integrals of a resonant Hamiltonian system2011

    • Author(s)
      Masafumi Yoshino
    • Organizer
      Formal and Analytic Solutions of Differential and Differene Equations(招待講演)
    • Place of Presentation
      Bedlewo (Poland)
    • Related Report
      2011 Research-status Report
  • [Presentation] Monodromy property of analytic non integrable Hamiltonian system2011

    • Author(s)
      Masafumi Yoshino
    • Organizer
      The 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications(招待講演)
    • Place of Presentation
      Hiroshima (Japan)
    • Related Report
      2011 Research-status Report
  • [Remarks]

    • URL

      http://home.hiroshima-u.ac.jp/yoshinom/

    • Related Report
      2013 Final Research Report
  • [Remarks] Research and Papers (研究成果報告)

    • URL

      http://home.hiroshima-u.ac.jp/yoshinom/

    • Related Report
      2013 Annual Research Report
  • [Remarks] Research and Papers (研究成果報告)

    • URL

      http://home.hiroshima-u.ac.jp/yoshinom/

    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://home.hiroshima-u.ac.jp/yoshinom/

    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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