Growth estimates for meromorphic solutions of higher order algebraic differential equations

Abstract: Pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations are obtained. A generalization of this result to higher order equations is also given. We discuss the related question of when for a given class X of meromorphic functions in the unit disc, defined by means of the spherical derivative and integer $n$, $n>1$, condition $f^n \in X$ implies $f \in X$. An affirmative answer to this is given in the case of UBC and some other classes. However, there are classes when the answer is negative.

complex variablesdynamical systems

Audience: researchers in the topic

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