Please use this identifier to cite or link to this item:
Type: Artigo de periódico
Title: Poincaré-hopf And Morse Inequalities For Lyapunov Graphs
Author: Bertolim M.A.
Mello M.P.
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.
Rights: fechado
Identifier DOI: 10.1017/S0143385704000483
Date Issue: 2005
Appears in Collections:Unicamp - Artigos e Outros Documentos

Files in This Item:
File Description SizeFormat 
2-s2.0-13444302714.pdf516.53 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.