Symplectically degenerate maxima via generating functions

We provide a simple proof of a theorem due to Nancy Hingston, asserting that symplectically degenerate maxima of any Hamiltonian diffeomorphism $\phi $ of the standard symplectic $2d$ -torus are non-isolated contractible periodic points or their action is a non-isolated point of the average-action spectrum of $\phi $ . Our argument is based on generating functions.