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Studies on complex dynamics of transcendental entire functions

Research Project

Project/Area Number 19540190
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, 教育研究部・自然科学系, 教授 (50220108)

Co-Investigator(Kenkyū-buntansha) TANIGUCHI Masahiko  奈良女子大学, 理学部, 教授 (50108974)
TOHGE Kazuya  金沢大学, 自然科学研究科, 准教授 (30260558)
ISHIZAKI Katsuya  日本工業大学, 工学部, 教授 (60202991)
KATO Kazuhisa  高知大学, 教育研究部・自然科学系, 教授 (20036578)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords複素解析 / 複素力学系 / 超越整関数 / 複素誤差関数 / 特異値 / 双曲成分 / 函数論 / 漸近値 / Schroeder方程式 / Siegel円板 / 構造有限型整関数 / 解析学 / 関数論 / ジーゲル円板 / ジュリア集合 / ファトウ集合 / 値分布論
Research Abstract

From the view point of the difference between dynamics of rational functions and those of transcendental entire functions, I mainly studied complex dynamics of transcendental entire functions. Singular values play important roles in studying complex dynamics. They are critical values or asymptotic values and the latter appear in the only case of transcendental entire functions. I investigated families of entire functions with two singular values and obtained some results on hyperbolic components of the parameter spaces. Furthermore, I showed a relationship between unbounded Siegel disks and asymptotic values, if transcendental entire functions have Siegel disks.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (28 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (12 results) (of which Peer Reviewed: 7 results) Presentation (12 results) Remarks (4 results)

  • [Journal Article] Meromorphic solutions of functional equations f(G(z))=R(f(z))2011

    • Author(s)
      K.Ishizaki, S.Morosawa
    • Journal Title

      Complex Var.Elliptic Equ.

      Volume: (投稿中 掲載確定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Siegel disks of transcendental entire functions and singular values2010

    • Author(s)
      諸澤俊介
    • Journal Title

      数理解析研究所講究録 1699

      Pages: 68-72

    • Related Report
      2010 Final Research Report
  • [Journal Article] Semi-conjugate functions in the complex plane2010

    • Author(s)
      Katsuya Ishizaki, Shunsuke Morosawa, Mitsunori Yakou
    • Journal Title

      Report of Researches Nippon Institute of Technology 39

      Pages: 142-145

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Journal Article] Siegel disks of transcendental entire functions and singular values2010

    • Author(s)
      諸澤俊介
    • Journal Title

      数理解析研究所講究録

      Volume: 1699 Pages: 68-72

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semi-conjugate functions in the complex plane2010

    • Author(s)
      Katsuya Ishizaki
    • Journal Title

      Report of Researches Nippon Institute of Technology 39

      Pages: 142-145

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Dynamics of structurally finite entire functions with two singular values, Comput.2009

    • Author(s)
      Shunsuke Morosawa, Masahiko Taniguchi
    • Journal Title

      Methods Funct. Theory 9

      Pages: 185-198

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dynamics of structurally finite entire functions with two singular values2009

    • Author(s)
      Shunsuke Morosawa, Masahiko Taniguchi
    • Journal Title

      Comput. Methods Funct.Theory 9

      Pages: 185-198

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Dynamics of structurally finite entire functions with two singular values2009

    • Author(s)
      Shunsuke Morosawa, Masahiko Taniguchi
    • Journal Title

      Comput. Methods Funct. Theory 9

      Pages: 185-198

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dynamics of structurally finite entire functions with two singular values2008

    • Author(s)
      Shunsuke Morosawa and Masahiko Taniguchi
    • Journal Title

      Comput.Methods Funct.Theory (発表確定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The parameter space of Error functions of the form $a\int^{z}_{0}e^{-w^{2}}dw$2007

    • Author(s)
      Shunsuke Morosawa
    • Journal Title

      Complex Analysis and Potential Theory, Proceedings of the Conference Satellite to ICM2006

      Pages: 174-177

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] The parameter space of Error functions of the form $a\int^{z}_{0}e^{-w^{2}}dw$2007

    • Author(s)
      Shunsuke Morosawa
    • Journal Title

      Proceedings of the Conference Satellite to ICM 2006

      Pages: 174-177

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Meromorphic solutions of functional equations $f(G(z))=R(f(z))$, Complex Var.

    • Author(s)
      Katsuya Ishizaki, Shunsuke Morosawa, Mitsunori Yakou
    • Journal Title

      Elliptic Equ. 「投稿中(掲載確定)」

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Presentation] Some questions on Schr {o} der functions2010

    • Author(s)
      諸澤俊介
    • Organizer
      複素力学系とその関連分野の総合的研究
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2010-12-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Some questions on Schroeder functions2010

    • Author(s)
      諸澤俊介
    • Organizer
      複素力学系とその関連分野の総合的研究
    • Place of Presentation
      京都大学理学部(京都府)
    • Year and Date
      2010-12-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] 超越関数特異値と複素力学系2010

    • Author(s)
      諸澤俊介
    • Organizer
      「等角写像論・値分布論」合同研究集会
    • Place of Presentation
      コラッセふくしま
    • Year and Date
      2010-12-04
    • Related Report
      2010 Final Research Report
  • [Presentation] 超越関数の特異値と複素力学系2010

    • Author(s)
      諸澤俊介
    • Organizer
      「等角写像論・値分布論」合同研究集会
    • Place of Presentation
      コラッセふくしま(福島県)
    • Year and Date
      2010-12-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Siegel disks of transcendental entire functions and singular values2009

    • Author(s)
      諸澤俊介
    • Organizer
      複素力学系とその関連分野の総合的研究
    • Place of Presentation
      京都大学大学院人間・環境学研究科
    • Year and Date
      2009-12-16
    • Related Report
      2010 Final Research Report 2009 Annual Research Report 2009 Self-evaluation Report
  • [Presentation] Meromorphic Solutions of Functional equations $f(G(z))=R(f(z))$2009

    • Author(s)
      石崎克也
    • Organizer
      等角写像論・値分布論合同研究集会
    • Place of Presentation
      東北大学
    • Year and Date
      2009-12-05
    • Related Report
      2010 Final Research Report
  • [Presentation] Meromorphic Solutions of Functional equations f(G(z))=R(f(z))2009

    • Author(s)
      石崎克也
    • Organizer
      「等角写像論・値分布論」合同研究集会
    • Place of Presentation
      東北大学
    • Year and Date
      2009-12-05
    • Related Report
      2009 Annual Research Report 2009 Self-evaluation Report
  • [Presentation] Bifurcations of error functions with real coefficients2008

    • Author(s)
      諸澤俊介
    • Organizer
      Aspects of Transcendental Dynamics
    • Place of Presentation
      Jacobs University Bremen, Germany
    • Year and Date
      2008-06-19
    • Related Report
      2010 Final Research Report
  • [Presentation] Bifurcations of error functions with real coefficients2008

    • Author(s)
      Shunsuke Morosawa
    • Organizer
      Aspects of Transcendental Dynamics
    • Place of Presentation
      Jacobs University Bremen
    • Year and Date
      2008-06-19
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Bifurcations of error functions with real coefficients2008

    • Author(s)
      諸澤 俊介
    • Organizer
      Aspects of Transcendental Dynamics
    • Place of Presentation
      Jacobs University Bremen, Germaney
    • Year and Date
      2008-06-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] Bifurcations of error functions with real coefficients2007

    • Author(s)
      諸澤俊介
    • Organizer
      複素力学系とその周辺分野の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-09-03
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report 2007 Annual Research Report
  • [Presentation] Dynamics of complex error functions2007

    • Author(s)
      諸澤俊介
    • Organizer
      The 15th International Conference on Finite or Infinite Dimensional Complex Analysis and Application
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2007-07-31
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report 2007 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.math.kochi-u.ac.jp/morosawa/index.html

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.math.kochi-u.ac.jp/morosawa/index.html

    • Related Report
      2010 Annual Research Report
  • [Remarks] ホームページ

    • URL

      http://www.math.kochi-u.ac.jp/morosawa/index.html

    • Related Report
      2009 Self-evaluation Report
  • [Remarks]

    • URL

      http://www.math.kochi-u.ac.jp/morosawa/index.html

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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