Connection matrices for Morse-Bott flows

Abstract

A Connection Matrix Theory approach is presented for Morse-Bott flows $\varphi$ on smooth closed $n$-manifolds by characterizing the set of connection matrices in terms of Morse-Smale perturbations. Further results are obtained on the effect on the set of connection matrices $\mathcal{CM}(S)$ caused by changes in the partial orderings and in the Morse decompositions of an isolated invariant set $S$.