Katrin Gelfert, Feliks Przytycki, Michal Rams, Juan Rivera-Letelier
Published 2010-12-12Version 1
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.
Lyapunov spectrum for rational maps
Lyapunov spectrum for Hénon-like maps at the first bifurcation
Lyapunov spectrum with constant sign
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