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Fatou-Julia theory on transcendental semigroups II

Published online by Cambridge University Press:  17 April 2009

Kin-Keung Poon
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong e-mail: kkpoon@math.hkbu.edu.hk
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Abstract

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In this paper, we extend our theories on the dynamics of transcendental semigroups. Several properties of Fatou and Julia sets of transcendental semigroups will be explored.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Bergweiler, W., ‘Iteration of meromorphic functions’, Bull. Amer. Math. Soc. 29 (1993), 151188.CrossRefGoogle Scholar
[2]Fatou, P., ‘Sur les equations fonctionelles’, Bull. Soc. Math. France 47 (1919), 161271; 48 (1920), 33–94.Google Scholar
[3]Fatou, P., ‘Sur l'iteration des fonctions transcendants entieres’, Acta. Math. 47 (1926), 337360.CrossRefGoogle Scholar
[4]Gross, F., Factorization of meromorphic functions (Naval Research Laboratory, U.S. Government Printing Office, Washington D.C., 1972).Google Scholar
[5]Hinkkanen, A. and Martin, G.J., ‘The dynamics of semigroups of rational functions I’, Proc. London. Math. Soc. (3) 73 (1996), 358384.Google Scholar
[6]Hinkkanen, A. and Martin, G.J., ‘Julia sets of rational semigroups’, Math. Z. 222 (1996), 161169.CrossRefGoogle Scholar
[7]Julia, G., ‘Sur l'iteration des fonctions rationelles’, J. Math. Pures. Appl. 4 (1918), 47245.Google Scholar
[8]Julia, G., ‘Sur la permutabilite des fractions rationelles’, Ann. Sci. Ecole Norm. Sup. 39 (1922), 131215.Google Scholar
[9]Nevanlinna, R., Analytic functions, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen 162 (Springer-Verlag, Berlin, Heidelberg, New York, 1970).CrossRefGoogle Scholar
[10]Poon, K.K., ‘Dynamics on transcendental semigroups’, Technical report in the Hong Kong Baptist University 173 (1998).Google Scholar
[11]Poon, K.K., ‘Fatou-Julia theory on transcendental semigroups’, Bull. Austral. Math. Soc. 58 (1998), 403410.CrossRefGoogle Scholar
[12]Poon, K.K. and Yang, C.C., ‘Dynamics of two permutable transcendental entire functions’, Ann. Polon. Math. 68 (1998), 159163.CrossRefGoogle Scholar
[13]Zhou, W.M. and Ren, F.Y., ‘The Julia sets of the random iterated systems by some rational functions’, Chinese Sci. Bull. 37 (1992), 969971.Google Scholar
[14]Zhou, W.M. and Ren, F.Y., ‘The Julia sets of the random iterated systems by transcendental functions’, Chinese Sci. Bull. 38 (1993), 289290.Google Scholar