AI 中文总结
本文针对具有有界类型无理不动点的二次多项式，通过引入近退化机制，获得了伪气泡大小和正则性的一致界，为中性重整化的组合刚性提供了关键基础。
AI 中文摘要
给定一个具有有界类型无理非游荡不动点的二次多项式，气泡是其 Siegel 盘的迭代原像。类似于伪 Siegel 盘，通过填充抛物型峡湾，可以从气泡构造伪气泡。我们引入了控制这些伪气泡在深层尺度上几何形状的 $\alpha'$-动力学中的近退化机制。因此，我们获得了与旋转数无关的伪气泡大小和正则性的一致界。在 [DLL] 中，与 Lyubich 合作，这一结果作为建立一致蝴蝶界以及最终中性重整化完全吸引子的组合刚性的必要组成部分。
英文摘要
Given a quadratic polynomial with an irrationally indifferent fixed point of bounded type, a bubble is an iterated preimage of its Siegel disk. Similar to pseudo-Siegel disks, one constructs pseudo-bubbles from bubbles by filling in parabolic fjords. We introduce the near-degenerate regime for the $α'$-Dynamics controlling the geometry of these pseudo-bubbles in deep scale. Consequently, we obtain uniform bounds on the size and regularity of pseudo-bubbles independent of the rotation number. In [DLL], jointly with Lyubich, this result serves as a necessary ingredient for establishing uniform butterfly bounds and ultimately the combinatorial rigidity of the full attractor of neutral renormalization.
Comments33 pages, 11 figures
