  This is a survey talk on the ICMS conference "Resonances of complex
dynamics", 9-13 July 2018. Three examples which show how dynamical
considerations lead to new results in complex function theory are discussed.
These examples are: a) a refinement of of the Wiman-Valiron method, b) the
proof of Hayman's conjecture on the value distribution of derivatives of
meromorphic functions, and c) a new simplified proof of the result of Lin and
Wang on the number of critical points of the Green function on a torus.
