论文标题
均匀的先验边界进行中性重归于
Uniform a priori bounds for neutral renormalization
论文作者
论文摘要
我们证明统一的``伪siegel''是有界类型的Siegel磁盘的先验界限，该磁盘在所有尺度上都均一范围内对其边界的振荡进行了统一的控制。结果，我们构建了母亲刺猬，该刺猬控制了任何具有中性周期性点的二次多项式后临界设置，并表明该刺猬具有类似星形的结构。伪siegel界限意味着该部门重新归一化的先验界限，这提供了将Siegel/Pacman重生理论扩展到所有近乎中性二次多项式的机会。二次多项式以外的各种应用也正在进行中。
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.
