Rocky Mountain Journal of Mathematics

Dynamics of Permutable Transcendental Entire Functions

Xiaoling Wang, Xinhou Hua, Chung-Chun Yang, and Degui Yang

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 36, Number 6 (2006), 2041-2055.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04] 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets

Complex dynamics Julia set permutable transcendental entire functions


Wang, Xiaoling; Hua, Xinhou; Yang, Chung-Chun; Yang, Degui. Dynamics of Permutable Transcendental Entire Functions. Rocky Mountain J. Math. 36 (2006), no. 6, 2041--2055. doi:10.1216/rmjm/1181069360.

Export citation


  • I.N. Baker, Wandering domains in the iteration of entire functions, Proc. London Math. Soc. 49 (1984), 563-576.
  • W. Bergweiler, Iteration of meromorphic functions, Bull. Amer. Math. Soc. 29 (1993), 151-188.
  • --------, On the Julia sets of analytic self-maps of the punctured plane, Analysis 15 (1995), 252-256.
  • W. Bergweiler and A. Hinkkanen, On semiconjugation of entire functions, Math. Proc. Cambridge Philos. Soc. 126 (1999), 565-574.
  • C.T. Chuang and C.C. Yang, Fix-points and factorization of meromorphic functions, World Scientific, Singapore, 1990.
  • A.E. Eremenko, On the iterates of entire functions, Dynam. Sys. Ergodic Theory, Banach Center Publ., Vol. 23, Polish Scientific Publ., Warsaw, 1989, pp. 339-345.
  • A.E. Eremenko and M.Yu. Lyubich, Dynamical properties of some classes of entire functions, Ann. Inst. Fourier 42 (1992), 989-1020.
  • P. Fatou, Sur les équations fonctionelles, Bull. Soc. Math. France 47 (1919), 161-271; 48 (1920), 33-94, 208-314.
  • --------, Sur l' itération des fonctions transcendentes entières, Acta Math. 47 (1926), 337-370.
  • F. Gross and C.F. Osgood, On fixed points of composite entire functions, J. London Math. Soc. 28 (1983), 57-61.
  • W.K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964.
  • X.H. Hua and C.C. Yang, Dynamics of transcendental functions, Gordon and Breach Science Publ., New York, 1998.
  • G. Julia, Mémoire sur l' itération des fractions rationnelles, J. Math. Pures Appl. 1 (1918), 47-245.
  • T. Kobayashi, Permutability and unique factorizability of certain entire functions, Kodai Math. J. 3 (1980), 8-25.
  • L.W. Liao and C.C. Yang, Julia sets of two permutable entire functions, J. Math. Soc. Jap. 1 (2004), 169-176.
  • --------, Some further results on the Julia sets of two permutable entire functions, Rocky Mountain J. Math. 35 (5) (2005), 1657-1674.
  • S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic dynamics, Cambridge Univ. Press, Cambridge, 2000.
  • T.W. Ng, Permutable entire functions and their Julia sets, Math. Proc. Cambridge Philos. Soc. 131 (2001), 129-138.
  • K.K. Poon and C.C. Yang, Dynamical behavior of two permutable entire functions, Ann. Polon. Math. 168 (1998), 159-163.
  • F.Y. Ren and W.S. Li, An affirmative answer to a problem of Baker, J. Fudan Univ. Natur. Sci. 36 (1997), 231-233.
  • W. Schmidt, On the periodic stable domains of permutable rational functions, Complex Variables Theory Appl. 17 (1992), 149-152.
  • X.L. Wang and C.C. Yang, On the Fatou components of two permutable transcendental entire functions, J. Math. Anal. Appl. 278 (2003), 512-526.
  • J.H. Zheng and Z.Z. Zhou, Permutability of entire functions satisfying certain differential equations, Tôhoku Math. J. 40 (1988), 323-330.
  • L.M. Zhu, D.G. Yang and X.L. Wang, On the Julia sets of permutable transcendental entire functions, J. Southeast Univ. 18 (2002), 270-273.