English

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 ψ\psi^\bullet-quadratic-like Siegel maps. In this form, the bounds are compatible with the ψ\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 ψ\psi^\bullet-quadratic-like structure degenerates around the Siegel disk on all geometric scales except on the ``transitional scales'' between two specific combinatorial levels.

Keywords

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