Uniform a priori bounds for neutral renormalization. Variation II: $ψ^\bullet$-ql Siegel maps
Authors
Dzmitry Dudko
Yusheng Luo
Mikhail Lyubich
Abstract
We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to $ψ^\bullet$-quadratic-like Siegel maps. In this form, the bounds are compatible with the $ψ$-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 $ψ^\bullet$-quadratic-like structure degenerates around the Siegel disk on all geometric scales except on the ``transitional scales'' between two specific combinatorial levels.
