  This paper deals with controllability properties of a cubic Ginzburg-Landau
equation with dynamic boundary conditions. More precisely, we prove a local
null controllability result by using a single control supported in a small
subset of the domain. In order to achieve this result, we firstly linearize the
system around the origin and we analyze it by the duality approach and an
appropriate Carleman estimate. Then, by using an inverse function theorem, the
local null controllability of the nonlinear system is proven.
