A generalized initial value problem for ODE's

Abstract

This paper introduces, up to the author's knowledge, for the first time the generalized initial value problem. In this problem, given an ordinary differential equation defined in some set, the initial conditions are mapped to a subset of that domain. This generalization allows some systems to radically change their properties, in fact some obstructions to asymptotic stability are get rid of by mapping the initial conditions set using modularity.