Fatou Components of Attracting Skew-Products
Fatou Components of Attracting Skew-Products
复制标题
Fatou 吸引偏斜产品的组成部分
DOI：
10.1007/s12220-017-9811-6
复制
发表时间：
2015
影响因子：
1.1
通讯作者：
I. M. Smit
中科院分区：
文献类型：
--
作者：
Han Peters;I. M. Smit
我们研究了两个复变量多项式斜积的游荡法头分量的存在性。2004年，Lilov （Fatou theory In two dimensions，博士论文，University of Michigan, 2004）证明了超吸引不变光纤附近不存在游荡域。2014年，Astorg等人（Ann Math, arXiv:1411.1188）证明了这一点。DS], 2014)，游荡域可以存在于抛物不变光纤附近。在Peters和Vivas （Math Z, arXiv:1408.0498, 2014）中，对几何吸引案例进行了研究，我们在这里继续研究。证明了次双曲吸引斜积的漫游域的不存在性；本课程包含Peters和Vivas中研究的地图（Math Z, arXiv:1408.0498, 2014）。利用不变光纤中Julia集的膨胀性质，证明了几乎所有光纤中临界轨道逃逸率的界。我们描述这些关键轨道的主要工具是不稳定流形的可能的奇异线性化映射。
We investigate the existence of wandering Fatou components for polynomial skew-products in two complex variables. In 2004, the non-existence of wandering domains near a super-attracting invariant fiber was shown in Lilov (Fatou theory in two dimensions, PhD thesis, University of Michigan, 2004). In 2014, it was shown in Astorg et al. (Ann Math, arXiv:1411.1188 [math.DS], 2014) that wandering domains can exist near a parabolic invariant fiber. In Peters and Vivas (Math Z, arXiv:1408.0498, 2014), the geometrically attracting case was studied, and we continue this study here. We prove the non-existence of wandering domains for subhyperbolic attracting skew-products; this class contains the maps studied in Peters and Vivas (Math Z, arXiv:1408.0498, 2014). Using expansion properties on the Julia set in the invariant fiber, we prove bounds on the rate of escape of critical orbits in almost all fibers. Our main tool in describing these critical orbits is a possibly singular linearization map of unstable manifolds.