# How Many Inflections are There in the Lyapunov Spectrum?

@article{Jenkinson2021HowMI, title={How Many Inflections are There in the Lyapunov Spectrum?}, author={Oliver Jenkinson and Mark Pollicott and Polina Vytnova}, journal={Communications in Mathematical Physics}, year={2021}, 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…

## One Citation

### Counting the Lyapunov inflections in piecewise linear systems

- MathematicsNonlinearity
- 2021

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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