Dynamical behavior of two permutable entire functions

Kin-Keung Poon; Chung-Chun Yang

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 2, page 159-163
  • ISSN: 0066-2216

Abstract

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

How to cite

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Kin-Keung Poon, and Chung-Chun Yang. "Dynamical behavior of two permutable entire functions." Annales Polonici Mathematici 68.2 (1998): 159-163. <http://eudml.org/doc/270412>.

@article{Kin1998,
abstract = {We show that two permutable transcendental entire functions may have different dynamical properties, which is very different from the rational functions case.},
author = {Kin-Keung Poon, Chung-Chun Yang},
journal = {Annales Polonici Mathematici},
keywords = {entire function; complex dynamics; permutable functions; permutable function; Fatou set; wandering domain},
language = {eng},
number = {2},
pages = {159-163},
title = {Dynamical behavior of two permutable entire functions},
url = {http://eudml.org/doc/270412},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Kin-Keung Poon
AU - Chung-Chun Yang
TI - Dynamical behavior of two permutable entire functions
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 2
SP - 159
EP - 163
AB - We show that two permutable transcendental entire functions may have different dynamical properties, which is very different from the rational functions case.
LA - eng
KW - entire function; complex dynamics; permutable functions; permutable function; Fatou set; wandering domain
UR - http://eudml.org/doc/270412
ER -

References

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  1. [1] I. N. Baker, Wandering domains in the iteration of entire functions, Proc. London Math. Soc. (3) 49 (1984), 563-576. Zbl0523.30017
  2. [2] W. Bergweiler, Iteration of meromorphic functions, Bull. Amer. Math. Soc. 29 (1993), 151-188. Zbl0791.30018
  3. [3] P. Fatou, Sur les équations fonctionnelles, Bull. Soc. Math. France 47 (1919), 161-271; 48 (1920), 33-94. Zbl47.0921.02
  4. [4] P. Fatou, Sur l'itération des fonctions transcendantes entières, Acta Math. 47 (1926), 337-360. Zbl52.0309.01
  5. [5] G. Julia, Sur l'itération des fonctions rationnelles, J. Math. Pures Appl. (7) 4 (1918), 47-245. Zbl46.0520.06
  6. [6] G. Julia, Sur la permutabilité des fractions rationnelles, Ann. Sci. Ecole Norm. Sup. 39 (1922), 131-215. Zbl48.0364.02
  7. [7] W. Schmidt, On the periodic stable domains of permutable rational functions, Complex Variables Theory Appl. 17 (1992), 149-152. 
  8. [8] J. H. Zheng and C. C. Yang, Permutability of entire functions, Kodai Math. J. 15 (1992), 230-235. Zbl0767.30024

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