Non-real zeros of linear differential polynomials in real meromorphic functions

It is shown that if $f$ or $1/f$ is a real entire function of infinite order of growth, with only real zeros, then $f''+\omega f$ has infinitely many non-real zeros for any $\omega > 0$.Comment: updated 27/09/1

Baker domains for Newton's method

We show that there exists an entire function without finite asymptotic values for which the associated Newton function tends to infinity in some invariant domain. The question whether such a function exists had been raised by Douady.Comment: 8 page