Lyapunov spectrum for exceptional rational maps

Details Lyapunov spectrum for exceptional rational maps Lyapunov spectrum for exceptional rational maps

2010-12-12

arxiv.org/abs/1012.2593v1

Mathematics

Dynamical Systems

Scientific paper

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 $\sigma$-finite conformal measures. This allows to extend previous results to exceptional rational maps.

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