On the Fatou components of two permutable transcendental entire functions ✩

Let f and g be two distinct permutable transcendental entire functions. Suppose further that q(g) = aq(f ) + b for some nonconstant polynomial q(z) and constants a ( = 0), b ∈ C. In this article, we will investigate the dynamical properties of f and g and show that they have the same Fatou sets with the same components.  2003 Elsevier Science (USA). All rights reserved