How Many Inflections are There in the Lyapunov Spectrum?

@article{Jenkinson2020HowMI,
  title={How Many Inflections are There in the Lyapunov Spectrum?},
  author={Oliver Jenkinson and Mark Pollicott and P. Vytnova},
  journal={Communications in Mathematical Physics},
  year={2020},
  volume={386},
  pages={1383 - 1411}
}
Iommi and Kiwi (J Stat Phys 135:535–546, 2009) 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 in Iommi and Kiwi (2009) 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 in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose… 
1 Citations

Counting the Lyapunov inflections in piecewise linear systems

Following the pioneering work of Iommi–Kiwi and Jenkinson–Pollicott–Vytnova, we continue to study the inflection points of the Lyapunov spectrum in this work. We prove that for any three-branch

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