  Decay to asymptotic steady state in one-dimensional logistic-like mappings is
characterized by considering a phenomenological description supported by
numerical simulations and confirmed by a theoretical description. As the
control parameter is varied bifurcations in the fixed points appear. We
verified at the bifurcation point in both; the transcritical, pitchfork and
period-doubling bifurcations, that the decay for the stationary point is
characterized via a homogeneous function with three critical exponents
depending on the nonlinearity of the mapping. Near the bifurcation the decay to
the fixed point is exponential with a relaxation time given by a power law
whose slope is independent of the nonlinearity. The formalism is general and
can be extended to other dissipative mappings.
