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arXiv · 2002.07781

How many inflections are there in the Lyapunov spectrum?

Oliver Jenkinson·Mark Pollicott·Polina Vytnova
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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.

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Oliver Jenkinson, Mark Pollicott, Polina Vytnova. 2020-02-18. How many inflections are there in the Lyapunov spectrum?. https://doi.org/10.1007/s00220-021-04161-4

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