• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2003 Fiscal Year Final Research Report Summary

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
Keywordscomplex dynamics / Fatou set / Julia set / transcendental entire function / stracturally finite entire function / complex error function / wandering domain / singular value
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

  • Research Products

    (14 results)

All Other

All Publications (14 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

URL: 

Published: 2005-04-19  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi