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2013 Fiscal Year Final Research Report

Analysis of the moduli space of rational maps from the point of view of complex dynamics

Research Project

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Project/Area Number 22540240
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research Institution防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群)

Principal Investigator

FUJIMURA Masayo  防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工, 総合教育学群, 講師 (00531758)

Project Period (FY) 2010-04-01 – 2014-03-31
Keywords解析学 / 複素力学系 / 数式処理 / 有理関数 / モジュライ空間
Research Abstract

One of the aim of this research is to give a faithful representation to the moduli space of rational maps, in order to apply to the theory of complex dynamical systems. For the moduli space of rational maps, a representation space and its compactification were obtained as one of the results of this research. Moreover, I solved problems of Goldberg that determine the number of Moebius equivalence classes corresponding to each sets of critical points explicitly when the degree is small.

  • Research Products

    (23 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (18 results) (of which Invited: 1 results)

  • [Journal Article] Inscribed ellipses and Blaschke products2013

    • Author(s)
      Masayo Fujimura
    • Journal Title

      Computational Methods and Function Theory

      Volume: 13 Pages: 557-573

    • DOI

      10.1007/s40315-013-0037-8

    • Peer Reviewed
  • [Journal Article] Explicit estimates on distance estimator method for Julia sets of polynomials2013

    • Author(s)
      Masayo Fujimura, Yasuhiro Gotoh, and Satoshi Yoshida
    • Journal Title

      Kodai Mathematical Journal

      Volume: 36 Pages: 491-507

    • DOI

      10.2996/kmj/1383660695

    • Peer Reviewed
  • [Journal Article] The generalized Bell locus of rational functions and problems of Goldberg, Topics in Finite or Infinite Dimensional Complex Analysis2013

    • Author(s)
      Masayo Fujimura, Mohaby Karima, and Masahiko Taniguchi
    • Journal Title

      Proceedings of the 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications

      Pages: 103-110

    • Peer Reviewed
  • [Journal Article] The Bell locus of rational functions and problems of Goldberg2012

    • Author(s)
      Masayo Fujimura, Mohaby Karima, and Masahiko Taniguchi
    • Journal Title

      Communications of Japan Society for Symbolic and Algebraic Computation

      Volume: 1 Pages: 67-74

    • URL

      http://www.jssac.org/Editor/CJssac/V01/V01_104.pdf

    • Peer Reviewed
  • [Journal Article] The shape of the dust-likeness locus of self-similar sets

    • Author(s)
      Miwa Aoki, Masayo Fujimura, and Masahiko Taniguchi
    • Journal Title

      Journal of Fractal Geometry

      Volume: (accepted)

    • Peer Reviewed
  • [Presentation] Blaschke積のなす包絡線とFussの定理の拡張2014

    • Author(s)
      藤村雅代
    • Organizer
      Risa/Asir Conference 2014
    • Place of Presentation
      神戸大学(兵庫、神戸市)
    • Year and Date
      2014-03-06
  • [Presentation] Blaschke products and bicentric polygons2014

    • Author(s)
      Masayo Fujimura
    • Organizer
      「等角写像論・値分布論」合同研究集会
    • Place of Presentation
      法政大学(東京都,千代田区)
    • Year and Date
      2014-01-11
  • [Presentation] Solving problems of Goldberg for rational maps on the projective space2013

    • Author(s)
      Masayo Fujimura
    • Organizer
      IMI共同利用研究集会数式処理研究と産学連携の新たな発展
    • Place of Presentation
      九州大学(福岡県,福岡市)
    • Year and Date
      2013-08-21
  • [Presentation] 有理関数のモジュライ空間のグローバルパラメータについて2013

    • Author(s)
      藤村雅代
    • Organizer
      日本数式処理学会第22回大会
    • Place of Presentation
      防衛大学校(神奈川県,横須賀市)
    • Year and Date
      2013-06-07
  • [Presentation] 複素平面上の幾何と数式処理2013

    • Author(s)
      藤村雅代
    • Organizer
      Risa/Asir Conference 2013 +第5回六甲博多計算代数会議
    • Place of Presentation
      神戸大学県,神戸市)
    • Year and Date
      2013-03-16
  • [Presentation] ブラシュケ積の幾何学的性質と計算実験2012

    • Author(s)
      藤村雅代
    • Organizer
      第5回日本数式処理学会基礎理論分科会&システム分科会合同研究会
    • Place of Presentation
      京都大学(京都府,京都市)
    • Year and Date
      2012-12-27
  • [Presentation] ブラシュケ積の幾何学的性質と双心多角形2012

    • Author(s)
      藤村雅代
    • Organizer
      数学ソフトウェアとフリードキュメントXV
    • Place of Presentation
      九州大学(福岡県福岡市)
    • Year and Date
      2012-09-17
  • [Presentation] The explicit descriptions of the ramification loci for the problems of Goldberg2012

    • Author(s)
      Masayo Fujimura
    • Organizer
      京都大学数理解析研究所研究集会数式処理研究の新たな発展
    • Place of Presentation
      京都大学数理解析研究所(京都府,京都市)
    • Year and Date
      2012-07-04
  • [Presentation] Chapple's formula and Blaschke products2012

    • Author(s)
      Masayo Fujimura
    • Organizer
      日本数式処理学会第21回大会
    • Place of Presentation
      山口大学(山口県,山口市)
    • Year and Date
      2012-06-08
  • [Presentation] Chapple-Eulerの定理の別証明とその拡張2012

    • Author(s)
      藤村雅代
    • Organizer
      Risa/Asir Conference 2012 +第4回六甲博多計算代数会議
    • Place of Presentation
      神戸大学(兵庫県,神戸市)
    • Year and Date
      2012-03-21
  • [Presentation] An extension of Chapple-Euler theorem2012

    • Author(s)
      Masayo Fujimura
    • Organizer
      第4回日本数式処理学会基礎理論分科会&システム分科会合同研究会
    • Place of Presentation
      仙台青葉カルチャーセンター(宮城県,仙台市)
    • Year and Date
      2012-01-21
  • [Presentation] The generalized Bell locus of rational functions and problems of Goldberg2011

    • Author(s)
      Masayo Fujimura
    • Organizer
      The 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      Hiroshima (Japan)
    • Year and Date
      2011-12-12
    • Invited
  • [Presentation] d次多項式のJulia集合の描画アルゴリズムとその精度評価2011

    • Author(s)
      吉田怜史, 藤村雅代, 後藤泰宏
    • Organizer
      日本数式処理学会第20回大会
    • Place of Presentation
      神戸大学(兵庫県,神戸市)
    • Year and Date
      2011-09-09
  • [Presentation] Julia集合の描画アルゴリズムの精度評価2011

    • Author(s)
      吉田怜史, 藤村雅代, 後藤泰宏
    • Organizer
      京都大学数理解析研究所研究集会数式処理研究の新たな発展
    • Place of Presentation
      京都大学数理解析研究所(京都府,京都市)
    • Year and Date
      2011-07-06
  • [Presentation] Julia集合の描画アルゴリズムと双曲距離2011

    • Author(s)
      吉田怜史, 藤村雅代, 後藤泰宏
    • Organizer
      Risa/Asir Conference 2011
    • Place of Presentation
      神戸大学(兵庫県,神戸市)
    • Year and Date
      2011-03-21
  • [Presentation] Computer experiment on solving Goldberg's problem2011

    • Author(s)
      Masayo Fujimura
    • Organizer
      Risa/Asir Conference 2011
    • Place of Presentation
      神戸大学(兵庫県,神戸市)
    • Year and Date
      2011-03-21
  • [Presentation] On the problem of Goldberg for the rational maps2010

    • Author(s)
      Masayo Fujimura
    • Organizer
      京都大学数理解析研究所研究集会Computer Algebra -- Design of Algorithms, Implementations and Applications
    • Place of Presentation
      京都大学数理解析研究所(京都府,京都市)
    • Year and Date
      2010-12-02
  • [Presentation] Boettcher関数の構成によるJulia集合の可視化2010

    • Author(s)
      吉田怜史, 藤村雅代, 後藤泰宏
    • Organizer
      京都大学数理解析研究所研究集会数式処理研究の新たな発展
    • Place of Presentation
      京都大学数理解析研究所(京都府,京都市)
    • Year and Date
      2010-07-09

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Published: 2015-07-16  

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