# Bifurcations in families of polynomial skew products

created by bianchi on 12 May 2018

[BibTeX]

preprint

Inserted: 12 may 2018
Last Updated: 12 may 2018

Year: 2018

ArXiv: 1801.01460 PDF

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.

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