Qualitative Theory of Differential Equations and Dynamics of Quadratic Rational Functions

Abstract

We study the qualitative theory of first order di fferential equations consisting of the iteration of complex quadratic rational functions and we focus on the configuration, namely location and stability, of simple equilibrium points which correspond to periodic points of the quadratic rational functions. Our main tools are properties of Julia sets of the quadratic rational functions and the Euler-Jacobi formula.