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Gradient-like flows on 3-manifolds

Published online by Cambridge University Press:  19 September 2008

K. A. de Rezende
K. A. de Rezende
Affiliation:
Departamento de Matemática, Universidade Estadual de Campinas, 13081–970 Campinas, Sāo Paulo, Brazil
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Abstract

In this paper, we determine properties that a Lyapunov graph must satisfy for it to be associated with a gradient-like flow on a closed orientable three-manifold. We also address the question of the realization of abstract Lyapunov graphs as gradient-like flows on three-manifolds and as a byproduct we prove a partial converse to the theorem which states the Morse inequalities for closed orientable three-manifolds. We also present cancellation theorems of non-degenerate critical points for flows which arise as realizations of canonical abstract Lyapunov graphs.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 3 , September 1993 , pp. 557 - 580
Copyright
Copyright © Cambridge University Press 1993

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