Author:
CRUZ R. N.,DE REZENDE K. A.
Abstract
The main purpose of this paper is to study the implications that the homology index of critical sets of smooth flows on closed manifolds M have on both the homology of level sets of M and the homology of M itself. The bookkeeping of the data containing the critical set information of the flow and topological information of M is done through the use of Lyapunov graphs. Our main result characterizes the necessary conditions that a Lyapunov graph must possess in order to be associated to a Morse–Smale flow. With additional restrictions on an abstract Lyapunov graph L we determine sufficient conditions for L to be associated to a flow on M.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
15 articles.
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