Submitted by ims_edit on Wed, 02/11/2026 - 12:40
preprint-id:
preprint-title:
Uniform a priori bounds for neutral renormalization. Variation II: -ql Siegel maps
preprint-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.
Submitted 30 September, 2025; v1 submitted 26 September, 2025; originally announced September 2025.
preprint-year:
2025
