2025/09/27 by Dudko, Dzmitry, Luo, Yusheng, Lyubich, Mikhail
#30C10 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2509.23031
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.