Published Paper
Inserted: 12 may 2018
Last Updated: 29 mar 2024
Journal: American Journal of Mathematics
Volume: 145
Number: 3
Pages: 861-898
Year: 2023
Doi: 10.1353/ajm.2023.a897498
Abstract:
We initiate a parametric study of families of polynomial skew products, i.e., polynomial endomorphisms of $\mathbb{C}^2$ of the form $F(z,w)=(p(z), q(z,w))$ that extend to endomorphisms of $\mathbb{P}^2(\mathbb{C})$. Our aim is to study and give a precise characterization of the bifurcation current and the bifurcation locus of such a family. As an application, we precisely describe the geometry of the bifurcation current near infinity, and give a classification of the hyperbolic components. This is the first study of a bifurcation locus and current for an explicit and somehow general family in dimension larger than 1.