Almost additive multifractal analysis for flows*Partially supported by FCT/Portugal through UID/MAT/04459/2019. CH was supported by FCT/Portugal through the Grant PD/BD/135523/2018. (21st June 2021) - Barreira, Luis; Holanda, Carllos
Abstract: Building on the construction of equilibrium measures, we establish a conditional variational principle for the multifractal spectra of an almost additive family with respect to a continuous flow Φ such that the entropy map μ ↦ h μ (Φ) is upper-semicontinuous. We also show that the spectrum is continuous and that in the case of hyperbolic flows the corresponding irregular sets have full topological entropy. More generally, we consider the spectrum for the u -dimension and obtain corresponding results.