A priori bounds for some infinitely renormalizable quadratic: IV. Elephant Eyes
Dynamical Systems
2026-01-30 v1
Abstract
In this paper we prove a priori bounds for an ``elephant eye'' combinatorics. Little -copies specifying these combinatorics are allowed to converge to the cusp of the Mandelbrot set. To handle it, we develope a new geometric tool: uniform thin-thick decompositions for bordered Riemann surfaces.
Cite
@article{arxiv.2601.21905,
title = {A priori bounds for some infinitely renormalizable quadratic: IV. Elephant Eyes},
author = {Jeremy Kahn and Misha Lyubich},
journal= {arXiv preprint arXiv:2601.21905},
year = {2026}
}