How Many Inflections are There in the Lyapunov Spectrum?

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