We describe all Lyapunov spectra that can be obtained by perturbing the
derivatives along periodic orbits of a diffeomorphism. The description is
expressed in terms of the finest dominated splitting and Lyapunov exponents
that appear in the limit of a sequence of periodic orbits, and involves the
majorization partial order. Among the applications, we give a simple criterion
for the occurrence of universal dynamics.Comment: A few improvements were made, based on the referee's suggestion