Stable foliations and CW-structure induced by a Morse-Smale gradient-like flow
Abstract
We prove that a Morse-Smale gradient-like flow on a closed manifold has a "system of compatible invariant stable foliations" that is analogous to the object introduced by Palis and Smale in their proof of the structural stability of Morse-Smale diffeomorphisms and flows, but with finer regularity and geometric properties. We show how these invariant foliations can be used in order to give a self-contained proof of the well-known but quite delicate theorem stating that the unstable manifolds of a Morse-Smale gradient-like flow on a closed manifold are the open cells of a -decomposition of .
Cite
@article{arxiv.2003.07134,
title = {Stable foliations and CW-structure induced by a Morse-Smale gradient-like flow},
author = {Alberto Abbondandolo and Pietro Majer},
journal= {arXiv preprint arXiv:2003.07134},
year = {2020}
}
Comments
57 pages, 1 figure. The list of references has been expanded and the discussion about the history of the problem and future perspectives has been improved thanks to the suggestions of some readers