On the dynamics of composition of entire functions
Copyright policy )On the dynamics of composition of entire functions
Let \(f\) and \(g\) be transcendental entire functions. It is known [\textit{W. Bergweiler} and \textit{Y. Wang}, Ark. Mat. 36, 31--39 (1998; Zbl 0906.30025); \textit{K.-K. Poon} and \textit{C.-C. Yang}, Proc. Japan Acad., Ser. A 74, No. 6, 87--89 (1998; Zbl 0919.30019)] that \(f(g)\) has a wandering Fatou component if and only if \(g(f)\) has a wandering Fatou component. In this paper a number of examples are given to show that there does not seem to be a relation between the dynamics of \(f\) and \(g\) and that of \(f(g)\). For example, a domain can be contained in a wandering Fatou component of \(f\) and of \(g\), but also lie in a periodic Fatou component of \(f(g)\), or the other way round. The examples are constructed using complex approximation theory.
- University of Jammu India
Fatou set, wandering domain, Entire functions of one complex variable (general theory), entire function, dynamics, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, Approximation in the complex plane, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
Fatou set, wandering domain, Entire functions of one complex variable (general theory), entire function, dynamics, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, Approximation in the complex plane, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
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