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.

中文翻译：

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吸引歪斜产品的法斗成分。

我们调查存在于两个复杂变量中的多项式偏积的游荡法图成分。2004年，在Lilov中证明了在超吸引不变纤维附近不存在游荡域（Fatou理论在二维中，密歇根大学博士学位论文，2004年）。2014年，它在Astorg等人的影片中显示。（Ann Math，arXiv：1411.1188 [math.DS]，2014年），抛物不变纤维附近可能存在漂移域。在Peters和Vivas（Math Z，arXiv：1408.0498，2014）中，研究了几何吸引情况，我们在此继续进行此研究。我们证明了不存在亚双曲线吸引偏积的漂移域。此类包含在Peters和Vivas中研究过的地图（Math Z，arXiv：1408.0498，2014）。使用不变光纤中Julia集上的展开特性，我们证明了几乎所有光纤中关键轨道的逃逸速率都有界。描述这些关键轨道的主要工具是不稳定流形的可能奇异的线性化图。