Study of structures of singular phenomena via complex global analysis

• Project/Area Number: 23540207
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hiroshima 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: ¥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.

Research Products

• [Journal Article] Global Properties of Evolutional Lotka-Volterra System (2013)
  • 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
  • Peer Reviewed
• [Journal Article] Smooth-integrable and analytic-nonintegrable resonant Hamiltonians (2013)
  • 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
  • Peer Reviewed
• [Journal Article] Asymptotic analysis to Goursat problems (2013)
  • 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
  • Peer Reviewed
• [Journal Article] Asymptotic analysis to Goursat problems (2013)
  • Author(s): Masafumi Yoshino
  • Journal Title: RIMS Kokyuuroku Bessatsu Volume: 37 Pages: 247-262
  • Peer Reviewed
• [Journal Article] Smooth-integrable and analytic- nonintegrable resonant Hamiltonians (2013)
  • Author(s): Masafumi Yoshino
  • Journal Title: RIMS Kokyuuroku Bessatsu Volume: 40 Pages: 177-189
  • Peer Reviewed
• [Journal Article] Analytic- nonintegrable resonant Hamiltonians which are integrable in a sector (2012)
  • 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
  • Peer Reviewed
• [Journal Article] Summability of first integrals of a C ω -nonintegrable resonant Hamiltonian system (2012)
  • Author(s): 吉野正史
  • Journal Title: Banach Center Publ Volume: Vol. 97 Pages: 169-178
  • DOI: 10.4064/bc97-0-13
  • Peer Reviewed
• [Journal Article] Sectorial solution to semilinear singular partial differential equation (2012)
  • 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
  • Peer Reviewed
• [Journal Article] Summability of first integrals of a C^ω-nonintegrable resonant Hamiltonian system (2012)
  • Author(s): Masafumi Yoshino
  • Journal Title: Publication in Banach Center Publ. Volume: 97 Pages: 169-178
  • Peer Reviewed
• [Journal Article] Analytic- nonintegrable resonant Hamiltonians which are integrable in a sector (2012)
  • Author(s): Masafumi Yoshino
  • Journal Title: Proceedings of the 19th ICFIDCAA Hiroshima 2011, Tohoku University Press Volume: 1 Pages: 85-96
  • Peer Reviewed
• [Journal Article] Asymptotic property of divergent formal solutions in linearization of singular vector field (2011)
  • Author(s): 吉野正史
  • Journal Title: Publications in RIMS Volume: Vol.47 No.4
  • Peer Reviewed
• [Journal Article] Werner Balser , Integrability of Hamiltonian systems and transseries expansions (2011)
  • 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
  • Peer Reviewed
• [Journal Article] Asymptotic property of divergent formal solutions in linearization of singular vector field (2011)
  • Author(s): Masafumi Yoshino
  • Journal Title: Publ. RIMS Ｋｙｏｔｏ Univ. Volume: 47 Pages: 937-958
  • Peer Reviewed
• [Presentation] Stokes geometry and summability in the linearization problem for a singular vector field (2013)
  • 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
• [Presentation] Singular perturbative analysis of Poincare's theorem for a singular vector field (2013)
  • 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
• [Presentation] Monodromy property of analytic non integrable Hamiltonian system (2013)
  • Author(s): Masafumi Yoshino
  • Organizer: Banach center, Poland
  • Place of Presentation: Bedlewo (Poland)
  • Invited
• [Presentation] Singular perturbative analysis of Poincar\'e's theorem for a singular vector field (2013)
  • Author(s): Masafumi Yoshino
  • Organizer: Banach center, Poland
  • Place of Presentation: Warsaw (Poland)
  • 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
• [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
  • 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
• [Presentation] Monodromy property of analytic non integrable Hamiltonian system (2011)
  • 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
• [Presentation] Summability of first integrals of a resonant Hamiltonian system (2011)
  • 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
• [Presentation] Summability of first integrals of a resonant Hamiltonian system (2011)
  • Author(s): Masafumi Yoshino
  • Organizer: Formal and Analytic Solutions of Differential and Differene Equations(招待講演)
  • Place of Presentation: Bedlewo (Poland)
• [Presentation] Monodromy property of analytic non integrable Hamiltonian system (2011)
  • 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)
• [Remarks]
  • URL: http://home.hiroshima-u.ac.jp/yoshinom/
• [Remarks] Research and Papers (研究成果報告)
  • URL: http://home.hiroshima-u.ac.jp/yoshinom/
• [Remarks] Research and Papers (研究成果報告)
  • URL: http://home.hiroshima-u.ac.jp/yoshinom/
• [Remarks]
  • URL: http://home.hiroshima-u.ac.jp/yoshinom/