Year: 2026
Type: preprint
Abstract: We prove that the postcritical set of every quadratic polynomial with a neutral fixed point has zero Lebesgue measure. In particular, no arithmetic condition on the rotation number is required. Our proof uses sector renormalization and the pseudo-Siegel bounds of Dudko-Lyubich to derive uniform distortion estimates for the renormalization change of variables. For sector renormalization towers, we also prove the same zero area statement for the associated postcritical set and the optimal Brjuno criterion for the interior of the associated Mother Hedgehog.
Source: arXiv (Cornell University)
Author: Lim, Willie Rush
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214733726