Multifractality and polygonal vortex filaments.

With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality of a family of generalized Riemann’s non-differentiable functions. These functions represent, in a certain limit, the trajectory of regular polygonal vortex filaments evolving according to the binormal flow, the classical model for vortex filaments dynamics. The result that I will present in this talk is that we determine for some of them the spectrum of singularities. The proofs rely on a careful design of Diophantine sets, which we study by using the Duffin-Schaeffer theorem and the Mass Transference Principle. This is a joint work with Daniel Eceizabarrena, Andrea Nahmod and Luis Vega.