Multifractal Spectrum and Thermodynamical Formalism of the Farey Tree

Let (Ω, µ) be a set of real numbers to which we associate a measure µ. Let α ≥ 0, let Ω α = {x ∈ Ω/α(x) = α}, where α is the concentration index defined by Halsey et al. [Halsey et al., 1986]. Let f H (α) be the Hausdorff dimension of Ω α. Let f L (α) be the Legendre spectrum of Ω, as defined in [Riedi and Mandelbrot, 1998]; and f C (α) the classical… (More)