论文标题
流浪稳定组件的出现
Emergence of wandering stable components
论文作者
论文摘要
我们证明存在C 2的C 2的一组局部密集的真实多项式自动形态；特别是，这解决了贝德福德（Bedford）和史密利（Smillie）在1991年报告的问题。这些FATOU组件具有非空的真实痕迹，它们的统计行为是历史悠久的。该证明基于表面真实映射的参数家族的几何模型。在一组密集的参数中，我们表明该模型的动力学显示了一个历史，较高的新兴，稳定的域。我们表明，该模型可以嵌入到h {é}非明显学位的家族中，也可以嵌入到Newhouse域中的表面差异性的一组开放且密集的5参数C R型，每2 $ \ le $ r $ r $ \ le $ $ $ $ $ $ $ $ $ $ \ y $ $ \ y = $ = $。这意味着Kiriki和Soma（2017）的工作的补充，这证明了C $ \ infty $和C $ω$ -case中的最后一个处理问题。主要困难是，此处仅沿有限维参数家族进行扰动。该证明基于[BER18]中引入的多赋形剂。
We prove the existence of a locally dense set of real polynomial automorphisms of C 2 displaying a wandering Fatou component; in particular this solves the problem of their existence, reported by Bedford and Smillie in 1991. These Fatou components have non-empty real trace and their statistical behavior is historical with high emergence. The proof is based on a geometric model for parameter families of surface real mappings. At a dense set of parameters, we show that the dynamics of the model displays a historical, high emergent, stable domain. We show that this model can be embedded into families of H{é}non maps of explicit degree and also in an open and dense set of 5-parameter C r-families of surface diffeomorphisms in the Newhouse domain, for every 2 $\le$ r $\le$ $\infty$ and r = $ω$. This implies a complement of the work of Kiriki and Soma (2017), a proof of the last Taken's problem in the C $\infty$ and C $ω$-case. The main difficulty is that here perturbations are done only along finite-dimensional parameter families. The proof is based on the multi-renormalization introduced in [Ber18].
