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

Studies the Newton map $N: mathbb{C} DEGREES2 ightarrowmathbb{C} DEGREES2$ associated to two equations in two unknowns, as a dynamical system. This title focuses on the first non-trivial case: two simultaneous quadratics, to intersect two conics. It proves among other things: the Russakovksi-Shiffman measure does not change the points of