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Lyapunov graph continuation

Published online by Cambridge University Press:  16 January 2003

M. A. BERTOLIM ,
M. P. MELLO  and
K. A. DE REZENDE
M. A. BERTOLIM
Affiliation:
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, Brazil
M. P. MELLO
Affiliation:
Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Campinas, SP, Brazil (e-mail: margarid@ime.unicamp.br)
K. A. DE REZENDE
Affiliation:
Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Campinas, SP, Brazil (e-mail: margarid@ime.unicamp.br)
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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 graphs considered may represent smooth flows on closed orientable n-manifolds, n \geq 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, the exact number of possible continuations of L are presented.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 1 , February 2003 , pp. 1 - 58
Copyright
2003 Cambridge University Press

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