The connection matrix in Morse-Smale flows. II

Abstract

Given a connection matrix for a Morse-Smale flow on a compact manifold, if there are no periodic orbits of equal or adjacent indices related in the partial order, we show that the periodic orbits can be replaced by doubly connected rest points in such a way that the given connection matrix induces the unique connection matrix for the resulting flow. It follows that for this class of flows, all nonuniqueness in the connection matrix is a consequence of the continuation theorem for connection matrices.