Flows and Foliations

Abstract

In this chapter, we investigate the global theory of ordinary differential equations (flows), referred to as O.D.E., and the Frobenius integrability condition for k-plane distributions (foliations). Although this latter topic concerns global partial differential equations (P.D.E.), our approach will be largely qualitative, with very few explicit partial differential equations in evidence. Unless otherwise indicated, all manifolds will have empty boundary.