JULIA LIMITING DIRECTIONS OF ENTIRE SOLUTIONS OF COMPLEX DIFFERENTIAL EQUATIONS

For entire or meromorphic function f , a value theta is an element of [0,2 pi) is called a Julia limiting direction if there is an unbounded sequence {z(n)} in the Julia set satisfying lim(n ->infinity) arg z(n) = theta. Our main result is on the entire solution f of P(z, f) F(z) f(s) = 0, where P(z, f) is a differential polynomial of f with entire coefficients of growth smaller than that of the entire transcendental F, with the integer s being no more than the minimum degree of all differential monomials in P(z, f). We observe that Julia limiting directions of f partly come from the directions in which F grows quickly.

Automated summary

The research focuses on the limiting directions of entire or meromorphic functions in Julia sets and their connection to differential polynomials.