ArticleOriginal scientific text

Title

Dynamical behavior of two permutable entire functions

Authors 1, 1

Affiliations

  1. Department of Mathematics, Hong Kong University of Science and Technology, Kowloon, Hong Kong

Abstract

We show that two permutable transcendental entire functions may have different dynamical properties, which is very different from the rational functions case.

Keywords

entire function, complex dynamics, permutable functions

Bibliography

  1. I. N. Baker, Wandering domains in the iteration of entire functions, Proc. London Math. Soc. (3) 49 (1984), 563-576.
  2. W. Bergweiler, Iteration of meromorphic functions, Bull. Amer. Math. Soc. 29 (1993), 151-188.
  3. P. Fatou, Sur les équations fonctionnelles, Bull. Soc. Math. France 47 (1919), 161-271; 48 (1920), 33-94.
  4. P. Fatou, Sur l'itération des fonctions transcendantes entières, Acta Math. 47 (1926), 337-360.
  5. G. Julia, Sur l'itération des fonctions rationnelles, J. Math. Pures Appl. (7) 4 (1918), 47-245.
  6. G. Julia, Sur la permutabilité des fractions rationnelles, Ann. Sci. Ecole Norm. Sup. 39 (1922), 131-215.
  7. W. Schmidt, On the periodic stable domains of permutable rational functions, Complex Variables Theory Appl. 17 (1992), 149-152.
  8. J. H. Zheng and C. C. Yang, Permutability of entire functions, Kodai Math. J. 15 (1992), 230-235.
Pages:
159-163
Main language of publication
English
Received
1997-02-17
Accepted
1997-06-05
Published
1998
Exact and natural sciences