2018/06/25 by Peter Imkeller, Gonçalo dos Reis, Imkeller, Peter +1
Mathematics · #37G35 #37H20 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Probability (math.PR) #advanced mathematical theories #primary 37D20 #secondary 37D45
paper · pdf · doi:10.48550/arxiv.1806.09585
openalex publication_date 2018/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute the Hausdorff dimension of a two-dimensional Weierstrass function, related to lacunary (Hadamard gap) power series, that has no Lévy area. This is done by interpreting it as a pullback attractor of a dynamical system based on the Baker transformation. A lower bound for the Hausdorff dimension is obtained by investigating the pushforward of the Lebesgue measure on the graph along scaled neighborhoods of stable fibers of the underlying dynamical system following the graph. Scaling ideas are crucial. They become accessible by self similarity properties of a mapping whose increments coincide with vertical distances on the stable fibers.