title: 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 × 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.
authors.affiliation: CORIA-UMR 6614 Normandie Université, CNRS-Université et INSA de Rouen, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France.
authors.forename: Christophe
authors.initials: C
authors.lastname: Letellier
authors.affiliation: Université de Lyon, ENTPE, Laboratoire Génie Civil et Bâtiment, 3 Rue Maurice Audin, F-69518 Vaulx-en-Velin Cedex, France.
authors.forename: Jean-Marc
authors.initials: JM
authors.lastname: Malasoma