  For an isotropic two-dimensional system, when the temperature is lowered
toward T=0, it has been found recently that, for the transition from the normal
to the superfluid state in the paramagnetic limit, the order parameter
describing the Fulde-Ferrell-Larkin-Ovchinnikov phase has an increasingly
complex structure with contributions from an increasing number of wavevectors.
This cascade of phase transitions is directly linked to the fact that, due to
the rotational invariance, all the wavevectors directions which can enter the
order parameter are degenerate. We study how this cascade of phase transitions
is modified when one takes into account the anisotropy arising in a real solid
state compound. For a simple model of anisotropy with elliptical dispersion
relation, we find surprisingly that the cascade of phase transitions is not
modified and the degeneracy with respect to the wavevector direction is still
present. When we take into account a deviation with respect to this elliptical
model, which is treated to first order in perturbation, we find that the
degeneracy is lifted and that, basically, a single wavevector is favored right
at the transition. However when one enters the superfluid phase, additional
wavevectors come in the order parameter and the cascade of transitions is still
present, though in a modified form.
