Abstract
For conformal mixing repellers such as Julia sets and nonlinear one-dimensional Cantor sets, we connect the pressure of a smooth transformation on the repeller with its generalized dimensions, entropies, and Liapunov exponents computed with respect to a set of equilibrium Gibbs measures. This allows us to compute the pressure by means of simple numerical algorithms. Our results are then extended to axiom-A attractors and to a nonhyperbolic invariant set of the line. In this last case, we show that a first-order phase transition appears in the pressure.
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Bessis, D., Paladin, G., Turchetti, G. et al. Generalized dimensions, entropies, and Liapunov exponents from the pressure function for strange sets. J Stat Phys 51, 109–134 (1988). https://doi.org/10.1007/BF01015323
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DOI: https://doi.org/10.1007/BF01015323