Perturbation of the Lyapunov spectra of periodic orbits

Jairo Bochi, Christian Bonatti

Published 2010-04-28, updated 2011-06-22Version 3

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.