Número:
46
Ano:
2001
Autor:
Maria Alice Bertolim
Margarida P. Mello
Ketty A. de Rezende
Abstract:
In this paper the Poincaré-Hopf inequalities are shown to be necessary and sufficient conditions for an abstract Lyapunov graph L to be continued to an abstract Lyapunov graph of Morse type. The Lyapunov graph considered represents smooth flows on closed orientable n-manifolds, n>2. The continuation which is presented by means of a constructive algorithm, is shown to be unique in dimensions two and three. In all other dimensions, upper bounds on the number of possible continuations of L are presented.
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