The dynamics of Topological Collet-Eckmann rational maps on Riemann sphere are well understood, due to the work of Przytycki, Rivera-Letelier and Smirnov. In this talk we study the dynamics of polynomial skew products of C^2. Let f be a polynomial skew products with an attracting invariant line L such that f restricted on L satisfies Topological Collet-Eckmann condition and a Weak Regularity condition. We show that the the Fatou set of f in the basin of L equals to the union of the basins of attracting cycles, and the Julia set of f in the basin of L has Lebesgue measure zero. As a consequence there are no wandering Fatou components in the basin of L (We remark that for some polynomial skew products with a parabolic invariant line L, there can exist a wandering Fatou component in the basin of L).
2016-2017，硕士学位，巴黎南大学 (Université Paris Sud)，导师：Romain Dujardin
2017-2020，博士学位在读，索邦大学 (Sorbonne Université)，导师：Romain Dujardin