On Limiting Directions of Julia Sets of Entire Solutions of Complex Differential Equations

Abstract

Assume that [see formula in PDF] is a transcendental entire function. The ray [see formula in PDF] is said to be a limiting direction of the Julia set [see formula in PDF] of [see formula in PDF] if there exists an unbounded sequence [see formula in PDF] such that [see formula in PDF]. In this paper, we mainly investigate the dynamical properties of Julia sets of entire solutions of the complex differential equations [see formula in PDF] and [see formula in PDF], where [see formula in PDF] is a differential polynomial in [see formula in PDF] and its derivatives, [see formula in PDF][see formula in PDF] and [see formula in PDF] are entire functions. We demonstrate the existence of close relationships Petrenko's deviations of the coefficients and the measures of limiting directions of entire solutions of the above two equations.