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Studies on complex dynamics of transcendental entire functions

Research Project

Project/Area Number 17540163
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKOCHI UNIVERSITY

Principal Investigator

MOROSAWA Shunsuke  KOCHI UNIVERSITY, Faculty of Science, Professor, 理学部, 教授 (50220108)

Co-Investigator(Kenkyū-buntansha) KATO Kazuhisa  KOCHI University, Faculty of Science, Professor, 理学部, 教授 (20036578)
TANIGUCHI Masahiko  Nara Women's University, Faculty of Science, Professor, 理学部, 教授 (50108974)
THOGE Kazuya  Kanazawa University, Graduate School of Natural Science and Technology, Associate Professor, 大学院自然科学研究科, 助教授 (30260558)
KISAKA Masashi  Kyoto University, Graduate School of Human and Environmental Studies, Associate Professor, 大学院人間・環境学研究科, 助教授 (70244671)
ISHIZAKI Katsuya  Nippon Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60202991)
中根 静男  東京工業大学, 工学部, 教授 (50172359)
Project Period (FY) 2005 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2005: ¥1,600,000 (Direct Cost: ¥1,600,000)
Keywordscomplex dynamics / transcendental entire function / complex error function / structurally finite entire / singular value / parameter space function / hyperbolic component / semihyperbolicity / ファトウ集合 / ジュリア集合 / 双曲型整関数
Research Abstract

The summary of research results is as follows.
1. Morosawa considers dynamics of complex error functions. In particular, he studies the parameter space of those functions with real coefficients. He obtains results on parabolic bifurcations along boundaries of hyperbolic components in the parameter space.
2. Complex error functions belong to the family of the structurally finite entire functions, which is defined by Taniguchi. Structurally finite entire functions with two singular values are classified into three types; complex error functions, simply decorated exponential maps and cubic polynomials. Morosawa and Taniguchi study the hyperbolic components in the parameter space of structurally finite entire functions with two singular values. They obtain results on hyperbolic component of capture type and prepare a paper.
3. Taniguchi considers covering structure of rational functions and entire functions and those dynamical structure and studies those relationships. He also gives a model of asymptotic Teichimiiller space.
4. Tohge improves the condition on the uniqueness theorem of meromorphic functions defined in the plane. In particular, he obtains a result on a relations of two functions which comes from conditions on angular domains.
5. Kisaka constructs transcendental entire functions with doubly connected wandering domain and, more generally, those with n-multiply connected wandering domains by using improved quasiconformal surgery. He also gives a characterization on semihyperbolicity of transcendental entire functions by using orbits of singular values.
8. Ishizaki studies a relation ship between properties on solutions of the Schroder equations in value distribution theory and in theory of complex dynamics.

Report

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

    (19 results)

All 2006 2005 Other

All Journal Article (19 results)

  • [Journal Article] The Teichmuller space of the ideal boundary2006

    • Author(s)
      M.Taniguchi
    • Journal Title

      Hiroshima Math. Journal 36

      Pages: 39-48

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Uniqueness theorems in an angular domain2006

    • Author(s)
      W.Lin, S.Mori, K.Tohge
    • Journal Title

      Tohoku Math. J. 58

      Pages: 509-527

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Borel and Julia directions of meromorphic Schroder functions II2006

    • Author(s)
      K.Ishizaki, N.Yanagihara
    • Journal Title

      Arch. Math 87

      Pages: 172-178

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The Teichmuller space of the ideal boundary2006

    • Author(s)
      M.Taniguchi
    • Journal Title

      Hiroshima Math.Journal Vol.36

      Pages: 39-48

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Uniqueness theorems in an angular domain2006

    • Author(s)
      W.Lin, S.Mori, K.Tohge
    • Journal Title

      Tohoku Math.J. Vol.58

      Pages: 509-527

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Borel and Julia directions of meromorphic Schroder functions II2006

    • Author(s)
      K.Ishizaki, N.Yanagihara
    • Journal Title

      Arch.Math Vol.87

      Pages: 172-178

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Borel and Julia directions of meromorphic Schroeder functions II2006

    • Author(s)
      K.Ishizaki, N.Yanagihara
    • Journal Title

      Arch. Math 87

      Pages: 172-178

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Covering structure and dynamical structure of a structurally finite entire function2005

    • Author(s)
      M.Taniguchi
    • Journal Title

      Kodai Math. Journal 28

      Pages: 430-438

    • NAID

      130003574502

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Borel and Julia directions of meromorphic Schroder functions2005

    • Author(s)
      K.Ishizaki, N.Yanagihara
    • Journal Title

      Math. Proc. Camb. Phil. Soc. 139

      Pages: 139-147

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Covering structure and dynamical structure of a structurally finite entire function2005

    • Author(s)
      M.Taniguchi
    • Journal Title

      Kodai Math.Journal Vol.28

      Pages: 430-438

    • NAID

      130003574502

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Borel and Julia directions of meromorphic Schroder functions2005

    • Author(s)
      K.Ishizaki, N.Yanagihara
    • Journal Title

      Math.Proc.Camb.Phil.Soc. Vol.139

      Pages: 139-147

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Dynamics of entire functions with two singular values2005

    • Author(s)
      S.Morosawa, M.Taniguchi
    • Journal Title

      数理解析研究所講究録 1447

      Pages: 130-137

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Structurally finite meromorphic functions2005

    • Author(s)
      M.Taniguchi
    • Journal Title

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

      Pages: 371-378

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Covering structure and dynamical structure of a structurally finite entire function,2005

    • Author(s)
      M.Taniguchi
    • Journal Title

      Kodai Math.J. 28

      Pages: 430-438

    • NAID

      130003574502

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Dynamics of a family of quadratic maps in the quaternion space2005

    • Author(s)
      S.Nakane
    • Journal Title

      International Journal of Bifurcation and Chaos 15

      Pages: 2535-2543

    • NAID

      110000272991

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Some examples of holomorphic curves in P^{n}(C) extremal to Cartan's defect relation2005

    • Author(s)
      K.Tohge
    • Journal Title

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

      Pages: 387-395

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Construction of multiply-connected wandering domains2005

    • Author(s)
      M.Kisaka, M.Shishikura
    • Journal Title

      数理解析研究所講究録 1447

      Pages: 108-123

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On multiply connected wandering domains of entire functions

    • Author(s)
      M.Kisaka, M.Shishikura
    • Journal Title

      Transcendental Dynamics and Complex Analysis (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On multiply connected wandering domains of entire functions

    • Author(s)
      M.Kisaka, M.Shishikura
    • Journal Title

      Transcendental Dynamics and Complex Analysis (in printing)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary

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

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