Julia sets of two permutable entire functions

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概要

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• In this paper first we prove that if f and g are two permutable tran-scendental entire functions satisfying f=f<SUB>1</SUB>(h) and g=g<SUB>1</SUB>(h), for some transcendental entire function h, rational function f<SUB>1</SUB> and a function g<SUB>1</SUB>, 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)e<SUP>q(z)</SUP>+c, where c is a constant, p a nonzero polynomial and q a nonconstant polynomial, or f(z)=\displaystyle ∈t<SUP>z</SUP>p(z)e<SUP>q(z)</SUP>dz, where p, q are nonconstant polynomials, such that f(g)=g(f) for a nonconstant entire function g, then J(f)=J(g).

• 社団法人 日本数学会の論文
• 2004-01-01

著者

• Yang Chung-chun

  Department Of Mathematics The Hong Kong University Of Science & Technology

• LIAO Liangwen

  Department of Mathematics Nanjing University

関連論文

• On a method of estimating derivatives in complex differential equations
• Julia sets of two permutable entire functions
• Value sharing of an entire function and its derivatives

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