2010/05/26 by Fathi Ben Nasr, Nasr, Fathi Ben, Jacques Peyrière +1
Economics, Econometrics and Finance · Mathematics · #11K55 #28A12 #28A78 #28A80 #Complex Systems and Time Series Analysis #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1005.4866
openalex publication_date 2010/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
New proofs of theorems on the multifractal formalism are given. They yield results even at points q for which Olsen's functions b(q) and B(q) differ. Indeed, we provide an example of measure for which functions b and B differ and for which the Hausdorff dimension of the level sets of the local Holder exponent are given by the Legendre transform of b and their packing dimension by the Legendre transform of B.