How many inflections are there in the Lyapunov spectrum?
Dynamical Systems
2021-08-18 v1
Abstract
Iommi & Kiwi showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture of Iommi & Kiwi by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question of Iommi & Kiwi by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.
Cite
@article{arxiv.2002.07781,
title = {How many inflections are there in the Lyapunov spectrum?},
author = {Oliver Jenkinson and Mark Pollicott and Polina Vytnova},
journal= {arXiv preprint arXiv:2002.07781},
year = {2021}
}
Comments
24 pages, 8 figures