Flow curvature manifolds for shaping chaotic attractors: Rossler-like systems

Jean-Marc Ginoux (1) , Christophe Letellier

1 PROTEE - Processus de Transfert et d'Echanges dans l'Environnement - EA 3819

Poincaré recognized that phase portraits are mainly structured around fixed points. Nevertheless, the knowledge of fixed points and their properties is not sufficient to determine the whole structure of chaotic attractors. In order to understand how chaotic attractors are shaped by singular sets of the differential equations governing the dynamics, flow curvature manifolds are computed. We show that the time dependent components of such manifolds structure Rossler-like chaotic attractors and may explain some limitation in the development of chaotic regimes.

Keywords: Chaos topology; Flow curvature manifold

Domains: Dynamical Systems [math.DS]

Jean-Marc Ginoux, Christophe Letellier. Flow curvature manifolds for shaping chaotic attractors: Rossler-like systems. Journal of Physics A: Mathematical and Theoretical, 2009, 42 (28), pp.285101. ⟨10.1088/1751-8113/42/28/285101⟩. ⟨hal-01056202⟩