Connection matrices for Morse-Bott flows. (English) Zbl 1362.37040
Summary: 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 \(S\).
MSC:
37B30 | Index theory for dynamical systems, Morse-Conley indices |
57R70 | Critical points and critical submanifolds in differential topology |