Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 631-656
Universidade Federal do Rio de Janeiro, Instituto de Matemática
Cidade Universitária - Ilha do Fundão, Rio de Janeiro 21945-909, Brazil;
gelfert 'at' im.ufrj.br
Instytut Matematyczny Polskiej Akademii Nauk
ul. Sniadeckich 8, 00-956 Warszawa, Poland;
feliksp 'at' impan.gov.pl
Instytut Matematyczny Polskiej Akademii Nauk
ul. Sniadeckich 8, 00-956 Warszawa, Poland;
rams 'at' impan.gov.pl
Pontificia Universidad Católica de Chile, Facultad de Matemáticas
Avenida Vicuña Mackenna 4860, Santiago, Chile;
riveraletelier 'at' mat.puc.cl
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 nonatomic invariant probability measures and is associated to certain \sigma-finite conformal measures. This allows to extend previous results to exceptional rational maps.
2010 Mathematics Subject Classification: Primary 37D25, 37D35, 37C45, 28D99, 37F10.
Key words: Lyapunov exponents, exceptional rational maps, pressure, conformal measures, Lyapunov spectrum, multifractal formalism.
Reference to this article: K. Gelfert, F. Przytycki, M. Rams and J. Rivera-Letelier: Lyapunov spectrum for exceptional rational maps. Ann. Acad. Sci. Fenn. Math. 38 (2013), 631-656.
doi:10.5186/aasfm.2013.3849
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