Flow curvature manifolds for shaping chaotic attractors: I. Roessler-like systems

Poincare 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 Roessler-like chaotic attractors and may explain some limitation in the development of chaotic regimes.