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 M are the open cells of a CW-decomposition of M.

Stable foliations and CW-structure induced by a Morse-Smale gradient-like flow

Majer P.
2021-01-01

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 M are the open cells of a CW-decomposition of M.
2021
Abbondandolo, A.; Majer, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1130896
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