H\"older spiral arcs
Classical Analysis and ODEs
2025-08-01 v3 Dynamical Systems
Abstract
We establish a quantitative necessary and sufficient condition for a spiral arc to be a H\"older arc. The class of spiral arcs contains the polynomial spirals studied by Fraser, and the elliptical spirals studied by Burrell-Falconer-Fraser. As an application, we recover the sharp result on the H\"older winding problem for polynomial spirals. Moreover, we provide a sharp exponent estimate for the H\"older classification of polynomial spirals, which coincides with the corresponding quasiconformal classification estimate, and improve certain exponent bounds of Burrell-Falconer-Fraser on the H\"older classification of elliptical spirals.
Cite
@article{arxiv.2502.18788,
title = {H\"older spiral arcs},
author = {Efstathios Konstantinos Chrontsios Garitsis and Vyron Vellis},
journal= {arXiv preprint arXiv:2502.18788},
year = {2025}
}
Comments
11 pages, proved a more general theorem in Section 3