Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/81717
Type: Artigo de periódico
Title: On the viability of local criteria for chaos
Author: Saa, A
Abstract: Recently, Zsczesny and Dobrowolski proposed a geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor sufficient for the occurrence of chaos. To this purpose, we introduce a class of chaotic two-dimensional systems with Gaussian curvature everywhere positive and, hence, locally stable. We show explicitly that chaotic behavior arises from some trajectories that reach certain non-convex parts of the boundary of the effective Riemannian manifold. Our result questions, once more, the viability of local, curvature-based criteria to predict chaotic behavior. (C) 2004 Elsevier Inc. All rights reserved.
Subject: chaos
integrability
Country: EUA
Editor: Academic Press Inc Elsevier Science
Rights: fechado
Identifier DOI: 10.1016/j.aop.20043.08.008
Date Issue: 2004
Appears in Collections:Unicamp - Artigos e Outros Documentos

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