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

Author:

Abbondandolo Alberto1ORCID,Majer Pietro2

Affiliation:

1. Ruhr-Universität Bochum, Fakultät für, Mathematik Universitätsstraße 150, 44780 Bochum, Germany

2. Università di Pisa, Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

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 [Formula: see text] are the open cells of a CW-decomposition of [Formula: see text].

Funder

Deutsche Forschungsgemeinschaft

Publisher

World Scientific Pub Co Pte Ltd

Subject

Geometry and Topology,Analysis

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Refinements of topological invariants of flows;Discrete & Continuous Dynamical Systems;2021

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