  Poincar\'e 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.
