Newton's Method Applied to Two Quadratic Equations in $\mathbb {C}^2$ Viewed as a Global Dynamical System - no. 891

The authors study the Newton map $N:\mathbb{C 2\rightarrow\mathbb{C 2$ associated to two equations in two unknowns, as a dynamical system.

They focus on the first non-trivial case: two simultaneous quadratics, to intersect two conics.

In the first two chapters, the authors prove among other things: