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Type: Artigo de periódico
Title: Poincare-Hopf and Morse inequalities for Lyapunov graphs
Author: Bertolim, MA
Mello, MP
de Rezende, KA
Abstract: Lyapunov graphs carry dynamical information of gradient-like flows as well as topological information of their phase space which is taken to be a closed orientable n-manifold. In this paper we will show that an abstract Lyapunov graph L(h(0), . . . , h(n), kappa) in dimension n greater than 2, with cycle number kappa, satisfies the Poincare-Hopf inequalities if and only if it satisfies the Morse inequalities and the first Betti number, gamma(1), is greater than or equal to kappa. We also show a continuation theorem for abstract Lyapunov graphs with the presence of cycles. Finally, a family of Lyapunov graphs L(h(0), . . . , h(n), kappa) with fixed pre-assigned data (h(0), . . . , h(n), kappa) is associated with the Morse polytope, P-kappa(h(0), . . . , h(n)), determined by the Morse inequalities for the given data.
Country: EUA
Editor: Cambridge Univ Press
Citation: Ergodic Theory And Dynamical Systems. Cambridge Univ Press, v. 25, n. 1, n. 39, 2005.
Rights: embargo
Identifier DOI: 10.1017/S0143385704000483
Date Issue: 2005
Appears in Collections:Unicamp - Artigos e Outros Documentos

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