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January, 2004 Julia sets of two permutable entire functions
Liangwen LIAO, Chung-Chun YANG
J. Math. Soc. Japan 56(1): 169-176 (January, 2004). DOI: 10.2969/jmsj/1191418700


In this paper first we prove that if f and g are two permutable transcendental entire functions satisfying f=f1(h) and g=g1(h), for some transcendental entire function h, rational function f1 and a function g1, which is analytic in the range of h, then F(g)F(f). Then as an application of this result, we show that if f(z)=p(z)eq(z)+c, where c is a constant, p a nonzero polynomial and q a nonconstant polynomial, or f(z)=zp(z)eq(z)dz, where p,q are nonconstant polynomials, such that f(g)=g(f) for a nonconstant entire function g, then J(f)=J(g).


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Liangwen LIAO. Chung-Chun YANG. "Julia sets of two permutable entire functions." J. Math. Soc. Japan 56 (1) 169 - 176, January, 2004.


Published: January, 2004
First available in Project Euclid: 3 October 2007

zbMATH: 1049.37036
MathSciNet: MR2027620
Digital Object Identifier: 10.2969/jmsj/1191418700

Primary: 30D35 , 58F23

Keywords: Fatou set , Julia set , permutable entire functions , prime , pseudo-prime

Rights: Copyright © 2004 Mathematical Society of Japan


Vol.56 • No. 1 • January, 2004
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