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|Type:||Artigo de periódico|
|Title:||Poincaré-hopf And Morse Inequalities For Lyapunov Graphs|
De Rezende K.A.
|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(h0,..., hn, κ) in dimension n greater than 2, with cycle number κ, satisfies the Poincaré-Hopf inequalities if and only if it satisfies the Morse inequalities and the first Betti number, γ1, is greater than or equal to κ. We also show a continuation theorem for abstract Lyapunov graphs with the presence of cycles. Finally, a family of Lyapunov graphs ℒ(h0,..., hn, κ) with fixed pre-assigned data (h0,..., hn, κ) is associated with the Morse polytope, Pκ (h0,..., hn), determined by the Morse inequalities for the given data.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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