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|Type:||Artigo de periódico|
|Title:||On the viability of local criteria for chaos|
|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.|
|Editor:||Academic Press Inc Elsevier Science|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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