Julia sets of two permutable entire functions

抄録

In this paper first we prove that if f and g are two permutable tran-scendental 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)e^q(z)+c, where c is a constant, p a nonzero polynomial and q a nonconstant polynomial, or f(z)=\displaystyle ∈t^zp(z)e^q(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).