Newton's Method Applied to Two Quadratic Equations in C2 Viewed as a Global Dynamical System

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: