For a class of dynamical systems, the cookie-cutter maps, we prove that the Lyapunov spectrum coincides with the map given by the Newton-Raphson method applied to the derivative of the pressure function.
@article{arxiv.1110.0842,
title = {The Lyapunov spectrum as the Newton method},
author = {Godofredo Iommi},
journal= {arXiv preprint arXiv:1110.0842},
year = {2015}
}