Uniform a priori bounds for neutral renormalization. Variation II: $\psi^\bullet$-ql Siegel maps
Dynamical Systems
2025-10-02 v2 Complex Variables
Abstract
We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to -quadratic-like Siegel maps. In this form, the bounds are compatible with the -quadratic-like renormalization theory and are easily transferable to various families of rational maps. The main theorem states that the degeneration of a Siegel disk is equidistributed among combinatorial intervals. This provides a precise description of how the -quadratic-like structure degenerates around the Siegel disk on all geometric scales except on the ``transitional scales'' between two specific combinatorial levels.
Cite
@article{arxiv.2509.23031,
title = {Uniform a priori bounds for neutral renormalization. Variation II: $\psi^\bullet$-ql Siegel maps},
author = {Dzmitry Dudko and Yusheng Luo and Mikhail Lyubich},
journal= {arXiv preprint arXiv:2509.23031},
year = {2025}
}
Comments
56 pages, 10 figures