Reduction of the Dynamics of a Bifurcation Problem Using Normal forms and Symmetries

Abstract

Let us consider a differential system

$$ \frac{\text{dX}}{{\text{dt}}}\quad { = }\quad {\text{F(X)}} $$

((1.1))

where X(t) lies in ℝⁿ or in some functional Hilbert space E, suitable for our physical problem. In this latter case we have to assume in what follows that the initial data problem has a unique solution in some real time interval [0,T], with all the usual regularity properties with respect to initial data and parameters.