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

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.

Publication Details

Journal
ArXiv.org
Published
2025-09-27
Primary Topic
Advanced oxidation water treatment
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

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

ArXiv.org
Advanced oxidation water treatment
article

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

article en

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.

ArXiv.org
Openalex Percentile: Top 47%
Advanced oxidation water treatment
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Uniform a priori bounds for neutral renormalization. Variation II: $ψ^\bullet$-ql Siegel maps · ArXiv.org (2025) | TGRS Research Map | TGRS