ABSTRACT
Introduction Although we obtained some explicit formulas for solutions of linear systems in Chapter 2, the results obtained suggest that there is very little chance of obtaining such formulas for more extensive classes of equations. For example, we obtained the explicit formula Pet J for a fundamental matrix of a linear homogeneous system with constant coefficients x ′ = Ax . However, even if we consider the slightly more general system x ′ = A(t)x where A(t) has period τ , the results obtained are no longer explicit formulas. Consequently, in studying larger classes of equations which include certain nonlinear equations, we must resign ourselves to obtaining limited information about the solutions. We will look for nonnumerical or “qualitative” properties of solutions. In this chapter we take the first steps in these qualitative studies by studying the qualitative properties of solutions of autonomous systems, which arise in many applications.
