  Dynamical systems often contain oscillatory forces or depend on periodic
potentials. Time or space periodicity is reflected in the properties of these
systems through a dependence on the parameters of their periodic terms. In this
paper we provide a general theoretical framework for dealing with these kinds
of systems, regardless of whether they are classical or quantum, stochastic or
deterministic, dissipative or nondissipative, linear or nonlinear, etc. In
particular, we are able to show that simple symmetry considerations determine,
to a large extent, how their properties depend functionally on some of the
parameters of the periodic terms. For the sake of illustration, we apply this
formalism to find the functional dependence of the expectation value of the
momentum of a Bose-Einstein condensate, described by the Gross-Pitaewskii
equation, when it is exposed to a sawtooth potential whose amplitude is
periodically modulated in time. We show that, by using this formalism, a small
set of measurements is enough to obtain the functional form for a wide range of
parameters. This can be very helpful when characterizing experimentally the
response of systems for which performing measurements is costly or difficult.
