  We study symplectic deformations of Gabor frames using the covariance
properties of the Heisenberg operators. This allows us to recover in a very
simple way known results. We thereafter propose a general deformation scheme by
Hamiltonian isotopies, which are paths of Hamiltonian flows. We define and
study in detail a weak notion of Hamiltonian deformations, using ideas from
semiclassical analysis due to Heller and Hagedorn. This method can be easily
implemented using symplectic integrators.
