Trajectories escaping to infinity in finite time

Abstract

If the function $f$ is transcendental and meromorphic in the plane, and either $f$ has finitely many poles or its inverse function has a logarithmic singularity over infinity, then the equation $\dot{z}=f(z)$ has infinitely many trajectories tending to infinity in finite increasing time

arXiv commentFinal version (to appear Proc. Amer. Math. Soc.)