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Research on dynamics of transcendental entire functions and polynomial semigroups based on dynamics of polynomials

Research Project

Project/Area Number 17K14212
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionTohoku Gakuin University (2022)
Ichinoseki National College of Technology (2017-2021)

Principal Investigator

Katagata Koh  東北学院大学, 教養学部, 准教授 (10529598)

Project Period (FY) 2017-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords複素力学系 / 超越整関数 / 擬多項式写像 / ジュリア集合 / 多項式半群
Outline of Final Research Achievements

The results of this research are as follows. (1) We constructed a transcendental entire function which has order zero containing dynamics of n quadratic polynomials locally, that is, containing n quadratic-like maps. (2) We constructed a transcendental entire function which has order zero containing dynamics of infinitely many quadratic polynomials locally, that is, containing infinitely many quadratic-like maps. (3) We constructed a transcendental entire function of arbitrarily slow growth containing dynamics of infinitely many polynomials of degree at least two locally, that is, containing infinitely many polynomial-like maps.

Academic Significance and Societal Importance of the Research Achievements

本研究では多項式の力学系を出発点として超越整関数の力学系特有の現象,特にファトウ集合やジュリア集合などの不変集合の位相的性質の解明と,擬多項式写像をキーワードにした力学系的性質の一般論の展開を目指した.本研究で得られた超越整関数はその構成方法から有限個または無限個の多項式の力学系を部分力学系として持っており,そのジュリア集合は多項式のジュリア集合のコピーを部分集合に持っている.上記(3)の超越整関数については無限個の多項式を扱っていることから,これまでにない新たな具体例が構成できたと言える.

Report

(7 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (15 results)

All 2022 2021 2020 2019 2018 2017

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (12 results)

  • [Journal Article] Entire functions of slow growth whose Julia set contains any infinite collection of quasiconformal copies of polynomial Julia sets2022

    • Author(s)
      Koh KATAGATA
    • Journal Title

      Journal of Difference Equations and Applications

      Volume: 28 Issue: 5 Pages: 605-637

    • DOI

      10.1080/10236198.2022.2070008

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Transcendental entire functions whose Julia sets contain any infinite collection of quasiconformal copies of quadratic Julia sets2019

    • Author(s)
      Katagata Koh
    • Journal Title

      Discrete and Continuous Dynamical Systems - Series A

      Volume: 39 Issue: 9 Pages: 5319-5337

    • DOI

      10.3934/dcds.2019217

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Entire functions whose Julia sets include any finitely many copies of quadratic Julia sets2017

    • Author(s)
      Koh KATAGATA
    • Journal Title

      Nonlinearity

      Volume: 30 Pages: 2360-2380

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Presentation] An example of functions of slow growth whose fast escaping set has Hausdorff dimension two2022

    • Author(s)
      片方 江
    • Organizer
      複素力学系と関連分野
    • Related Report
      2022 Annual Research Report
  • [Presentation] 無限個の擬多項式写像を含む超越整関数の構成2022

    • Author(s)
      片方 江
    • Organizer
      「等角写像・値分布論」合同研究集会
    • Related Report
      2022 Annual Research Report
  • [Presentation] 無限個の擬多項式写像を含む超越整関数の構成2021

    • Author(s)
      片方 江
    • Organizer
      Real, Complex and Functional Analysis Seminar 2020
    • Related Report
      2020 Research-status Report
  • [Presentation] Transcendental entire functions whose Julia sets contain any infinite collection of quasiconformal copies of polynomial Julia sets2021

    • Author(s)
      片方 江
    • Organizer
      2020年度「リーマン面・不連続群論」研究集会
    • Related Report
      2020 Research-status Report
  • [Presentation] Transcendental entire functions whose Julia sets contain any infinite collection of quasiconformal copies of polynomial Julia sets2020

    • Author(s)
      片方 江
    • Organizer
      複素力学系理論の総合的研究
    • Related Report
      2020 Research-status Report
  • [Presentation] Transcendental entire functions whose Julia sets contain any infinite collection of quasiconformal copies of quadratic Julia sets2019

    • Author(s)
      片方 江
    • Organizer
      日本数学会2019年秋季総合分
    • Related Report
      2019 Research-status Report
  • [Presentation] 無限個の2次擬多項式写像を含む超越整関数の構成2019

    • Author(s)
      片方 江
    • Organizer
      Real, Complex and Functional Analysis Seminar 2019
    • Related Report
      2019 Research-status Report
  • [Presentation] Transcendental entire functions whose Julia sets contain any infinite collection of quasiconformal copies of quadratic Julia sets2019

    • Author(s)
      片方 江
    • Organizer
      複素力学系の分岐と安定性の研究
    • Related Report
      2019 Research-status Report
  • [Presentation] 無限個の2次擬多項式写像を含む超越整関数の構成2018

    • Author(s)
      片方 江
    • Organizer
      Geometry of Riemann surfaces and related topics
    • Related Report
      2018 Research-status Report
  • [Presentation] 擬等角手術によって構成された超越整関数の位数2018

    • Author(s)
      片方 江
    • Organizer
      2017年度日本数学会東北支部会
    • Related Report
      2017 Research-status Report
  • [Presentation] Entire functions whose Julia sets include any finitely many copies of quadratic Julia sets2017

    • Author(s)
      片方 江
    • Organizer
      日本数学会2017年秋季総合分科会
    • Related Report
      2017 Research-status Report
  • [Presentation] Transcendental entire functions whose Julia sets include any infinitely many copies of quadratic Julia sets2017

    • Author(s)
      片方 江
    • Organizer
      平成29年度等角写像論・値分布論研究集会
    • Related Report
      2017 Research-status Report

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Published: 2017-04-28   Modified: 2024-01-30  

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