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Studies on complex dynamics of transcendental entire functions and singular values

Research Project

Project/Area Number 14540179
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, Associate Professor, 理学部, 助教授 (50220108)

Co-Investigator(Kenkyū-buntansha) TANIGUCHI Masahiko  Kyoto University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50108974)
KATO Kazuhisa  KOCHI UNIVERSITY, Faculty of Science, Professor, 理学部, 教授 (20036578)
NIIZEKI Shozo  KOCHI UNIVERSITY, Faculty of Science, Professor, 理学部, 教授 (60036572)
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)
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)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2003: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2002: ¥1,800,000 (Direct Cost: ¥1,800,000)
Keywordscomplex dynamics / Fatou set / Julia set / transcendental entire function / stracturally finite entire function / complex error function / wandering domain / singular value / 半双曲性
Research Abstract

The summary of research results is as follows.
1.Morosawa and taniguchi consider dynamics of structurally finite transcendental entire functions with two singular values. In particular, they consider structurally finite transcendental entire functions with two asymptotic values, which are so-called complex error functions. They investigate hyperbolic components of the moduli space of complex error functions with real coefficients. Furthermore Morosawa proves Fatou components of certain complex error functions have a common curve in their boundaries.
2.In dynamics of polynomials, there never exist Baker domains nor wandering domains. To the contrary, in that of transcendental entire functions, there may exists those. On the other hand, any transcendental entire function can be approximated by some sequences of polynomials in the sense of locally uniformly convergence. Morosawa considers the Caratheodory convergence of Fatou sets and the Hausdorff convergence of Julia sets of such sequence … More s of polynomials to a certain transcendental entire function which have a Baker domain and wandering domains.
3.Taniguchi considers structurally finite transcendental entire functions and investigates their covering structure and topological structure. He defines a new kind of the deformation space of a general entire function, and discuss about completeness and stability of such deformation spaces in case of structurally finite entire functions.
5.Tohge considers unique range sets for polynomials or rational functions. He also considers related results, including (i) rational functions that share three values, and (ii) sets which are almost(apart from exceptional cases) unique range seta for different classes of meromorphic functions.
7.Kisaka constructs ray tails for structurally finite transcendental entire functions. By using these rays, he investigates topological structures for structurally finite transcendental entire functions.
8.Kisaka constructs multiply connected wandering domains by using quasi-conformal surgeries. Less

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (26 results)

All Other

All Publications (26 results)

  • [Publications] S.Morosawa: "Semihyperbolic entire functions"Nonlinearity. 15. 1673-1684 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Morosawa: "The Caratheodory convergence of Fatou components of polynomials to Baker domains or wandering domains II"Proceedings of the 10th International Conference on Finite Dimensional Complex Analysis and Applications. 127-132 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Taniguchi: "Size of the Julia set of a structurally finite transcendental entire function"Math.Proc.Camb.Phil.Soc.. 135. 181-192 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Taniguchi, M.Jeong: "Bell representations of finitely connected planar domains"Proc.American Math.Soc.. 131. 2325-2328 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Ishizaki, I.Laine, S.Shimomura, K.Tohge: "Riccati differential equations with elliptic coefficients, II"Tohoku Mathematical Journal. 55. 99-108 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] G.G.Gundersen, K.Tohge: "Unique range sets for polynomials or rational functions"Progress in Analysis, Proceedings of the 3rd ISAAC Congress. 1. 235-246 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] W.Bergweiler, S.Morosawa: "Semihyperbolic entire functions"Nonlinearity. Vol.15. 1673-1684 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Morosawa: "The Garatheodory convergence of Fatou components of polynomials to Baker domains or wandering domains II"Proceedings of the 10th International Conference on Finite Dimensional Complex Analysis and Applications. 127-132 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Taniguchi: "Synthetic deformation space of an entire function"Contemporary Math.. Vol.303. 107-136 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Taniguchi: "Size of the Julia set of a structurally finite transcendental entire function"Math.Proc.Camb.Phil.Soc.. Vol.135. 181-192 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Jeong, M.Taniguchi: "Algebraic kernel functions and representation of planar domains"J.Korea Math.Soc.. Vol.40. 447-460 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Ishizaki, I.Laine, S.Shimomura, K.Tohge: "Riccati differential equations with elliptic coefficients, II"Tohoku Mathematical Journal. Vol.55. 99-108 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] G.G.Gundersen, K.Tohge: "Unique range sets for polynomials or rational functions"Progress in Analysis, Proceedings of the 3rd ISAAC Congress. Vol.1. 235-246 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] G.G.Gundersen, K.Tohge: "Entire and meromorphic solutions of f^5+g^5+h^5=1"Univ.Joensuu Dept.Math.Report series. Vol.6(in printing).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Morosawa: "The Caratheodory convergence of Fatou components of polynomials to Baker domains or wandering domains II"Proceedings of the 10th International Conference on Finite Dimensional Complex Analysis and Applications. 127-132 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Niizeki: "On a method to prove Stirling's formula"Tamsui Oxford J.Math.Sci.. 19. 117-120 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Taniguchi: "Size of the Julia set of a structurally finite transcendental entire function"Math.Proc.Camb.Phil.Soc.. 135. 181-192 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Taniguchi, M.Jeong: "Bell representations of finitely connected planar domains"Proc.American Math.Soc.. 131. 2325-2328 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Ishizaki, I.Laine, S.Shimo-mura, K.Tohge: "Riccati differential equations with elliptic coefficients, II"Tohoku Mathematical Journal. 55. 99-108 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] G.G.Gundersen, K.Tohge: "Unique range sets for polynomials or rational functions"Progress in Analysis, Proceedings of the 3rd ISAAC Congress. 1. 235-246 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] W.Bergweiler, S.Morosawa: "Semihyperbolic entire functions"Nonlinearity. 15. 1673-1684 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Niizeki, Y.Oishi: "On the convergence of sequence of sets and the continuity of measure"Mem. Fac. Sci. Kochi Univ. (Math.). 23. 9-17 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Taniguchi: "Synthetic deformation space of an entire function"Contemporary Math.. 303. 107-136 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Taniguchi: "Size of the Julia set of a structurally finite transcendental entire function"Math. Proc. Camb. Phil. Soc.. (印刷中).

    • Related Report
      2002 Annual Research Report
  • [Publications] G.G.Gundersen, K.Tohge: "Unique range sets for polynomials or rational functions"Proceedings of the 3rd ISAAC Congress. (印刷中). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Ishizaki, I.Laine, S.Shimomura, K.Tohge: "Riccati differential equations with elliptic coefficients, II"Tohoku Mathematical Journal. (印刷中). (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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