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arXiv · 1012.2593

Lyapunov spectrum for exceptional rational maps

Katrin Gelfert·Feliks Przytycki·Michal Rams·Juan Rivera-Letelier
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Abstract

We study the dimension spectrum for Lyapunov exponents for rational maps acting on the Riemann sphere and characterize it by means of the Legendre-Fenchel transform of the hidden variational pressure. This pressure is defined by means of the variational principle with respect to non-atomic invariant probability measures and is associated to certain $σ$-finite conformal measures. This allows to extend previous results to exceptional rational maps.

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Katrin Gelfert, Feliks Przytycki, Michal Rams, Juan Rivera-Letelier. 2010-12-12. Lyapunov spectrum for exceptional rational maps. https://arxiv.org/abs/1012.2593

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