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arXiv · 2509.23031

Uniform a priori bounds for neutral renormalization. Variation II: $\psi^\bullet$-ql Siegel maps

Dzmitry Dudko·Yusheng Luo·Mikhail Lyubich
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Abstract

We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to $\psi^\bullet$-quadratic-like Siegel maps. In this form, the bounds are compatible with the $\psi$-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 $\psi^\bullet$-quadratic-like structure degenerates around the Siegel disk on all geometric scales except on the ``transitional scales'' between two specific combinatorial levels.

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Dzmitry Dudko, Yusheng Luo, Mikhail Lyubich. 2025-09-27. Uniform a priori bounds for neutral renormalization. Variation II: $\psi^\bullet$-ql Siegel maps. https://arxiv.org/abs/2509.23031

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