Variational principles and mixed multifractal spectra (Q2723457)

This paper is devoted to the subshifts of finite type and repellers of \(C^{1+\varepsilon}\) conformal expanding maps. For such maps the authors prove that if \(\mu\) is an equilibrium measure with Hölder continuous potential, then 1) the functions \(D_E\) and \(E_D\) are real analytic, 2) the functions \(D_E\) and \(E_D\) are in general not convex and thus, they cannot be expressed as Legendre transforms where by \(D_E\) and \(E_D\) are denoted entropy spectrum for pointwise dimensions and dimension spectrum for local entropies respectively. These statements follow from a new ``conditional'' variational principle established by the authors. Moreover the authors provide an application to the multifractal analysis of limit sets of geometric constructions.