The energy function for gradient-like diffeomorphisms on 3-manifolds
type: Item
instance of: scholarly article
title: The energy function for gradient-like diffeomorphisms on 3-manifolds
zbMATH Open document ID: 1187.37022
DOI: 10.1134/S1064562408050165
author: François Laudenbach
author: V. Z. Grines
author: O. V. Pochinka
published in: Doklady Mathematics
publication date: 2010-01-12T00:00:00Z
review text: In 1978 Conley proved the existence of a continuous Lyapunov function for any flow on a smooth closed manifold and it is now regarded as the fundamental theorem of the dynamical systems. It is also known that for any Morse-Smale diffeomorphism the chain recurrent set coincides with the set of periodic orbits. The authors obtain existence conditions for self-indexing energy functions.
reviewed by: Yoshihide Kozai
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 37D15
zbMATH DE Number: 5656080
zbMATH Keywords: Lyapunov function
zbMATH Keywords: energy function
zbMATH Keywords: diffeomorphism
MaRDI profile type: Publication
cites work: Knots as topological invariants for gradient-like diffeomorphisms of the sphere \(S^3\)
cites work: Some wild cells and spheres in three-dimensional space
cites work: Q4180600
cites work: A mildly wild imbedding of an \(n\)-frame
cites work: New relations for Morse-Smale systems with trivially embedded one-dimensional separatrices
cites work: Energy Functions for Morse Smale Systems
cites work: Wild unstable manifolds
cites work: Q4226356
cites work: Differentiable dynamical systems
cites work: On gradient dynamical systems
full work available at URL: s1064562408050165
OpenAlex ID: W2082644677
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description: scientific article; zbMATH DE number 5656080