Perturbation of the Lyapunov spectra of periodic orbits

TL;DR

This paper characterizes how Lyapunov spectra of periodic orbits can be perturbed, linking the spectra to dominated splittings and Lyapunov exponents, and provides criteria for universal dynamics.

Contribution

It offers a comprehensive description of possible Lyapunov spectrum perturbations using dominated splittings and majorization, advancing understanding of dynamical stability.

Findings

Characterization of all Lyapunov spectra obtainable by perturbations.

Connection between spectra and dominated splittings.

Criterion for the emergence of universal dynamics.

Abstract

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.