中性重整化的均匀先验界
Uniform a priori bounds for neutral renormalization
AI总结：
本文证明有界型Siegel盘的均匀伪Siegel先验界，构造具有星状结构的母刺猬以控制二次多项式后临界集，并将Siegel/Pacman与近抛物重整化理论推广到所有近中性二次多项式。
摘要：
我们证明了有界型Siegel盘的均匀“伪Siegel”先验界，该界在所有尺度上对其边界的振荡给出均匀控制。作为推论，我们构造了控制任何具有中性周期点的二次多项式后临界集的“母刺猬”，并证明该刺猬具有星状结构。伪Siegel界蕴含扇形重整化的均匀先验界，这为将Siegel/Pacman重整化理论和近抛物重整化理论推广到所有近中性二次多项式提供了可能。超越二次多项式的各种应用也正在进行中。
英文摘要：
We prove uniform ``pseudo-Siegel'' a priori bounds for Siegel disks of bounded type that give a uniform control of oscillations of their boundaries in all scales. As a consequence, we construct the Mother Hedgehog controlling the postcritical set for any quadratic polynomial with a neutral periodic point and show that this hedgehog has a star-like structure. Pseudo-Siegel bounds imply uniform a priori bounds of the Sector Renormalization, which gives an opportunity to extend Siegel/Pacman Renormalization Theory and Near-Parabolic Renormalization Theory to all near-neutral quadratic polynomials. Various applications beyond quadratic polynomials are also underway.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
