Architecture of chaotic attractors for flows in the absence of any singular point

Abstract : Some chaotic attractors produced by three-dimensional dynamical systems without any singular point have now been identified, but explaining how they are structured in the state space remains an open question. We here want to explain-in the particular case of the Wei system-such a structure, using one-dimensional sets obtained by vanishing two of the three derivatives of the flow. The neighborhoods of these sets are made of points which are characterized by the eigenvalues of a 2 x 2 matrix describing the stability of flow in a subspace transverse to it. We will show that the attractor is spiralling and twisted in the neighborhood of one-dimensional sets where points are characterized by a pair of complex conjugated eigenvalues. We then show that such one-dimensional sets are also useful in explaining the structure of attractors produced by systems with singular points, by considering the case of the Lorenz system. Published by AIP Publishing.
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Article dans une revue
Chaos, American Institute of Physics, 2016, 26 (6), pp.063115. 〈10.1063/1.4954212〉
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Soumis le : jeudi 5 octobre 2017 - 15:36:49
Dernière modification le : samedi 27 octobre 2018 - 01:28:55

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Christophe Letellier, Jean-Marc Malasoma. Architecture of chaotic attractors for flows in the absence of any singular point. Chaos, American Institute of Physics, 2016, 26 (6), pp.063115. 〈10.1063/1.4954212〉. 〈hal-01611242〉

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