On the viability of local criteria for chaos |
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Authors: | Alberto Saa |
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Institution: | Departamento de Matemática Aplicada, IMECC—UNICAMP, C.P. 6065, 13083-970 Campinas, SP, Brazil |
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Abstract: | Recently, Zscze¸sny 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. |
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Keywords: | 05 45 Ac 45 10 Na |
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