Apr 2002 Carl Dettmann says that there is no need to use the 2(D+1) dimensional strategy - that Poincare section 2(D-1) search works better, is faster. The Poincare section is computed using the Henon's trick as written up in the "Maps" of the webbook. In order to determine the [2(D-1) x 2(D-1)] Poincare map stability matrix from the flow integration compute 2D Jacobian as for flow, then find the change in time needed to hit the Poincare section again, substitute back to remove one degree of freedom. The attached Kuramoto-Sivasinsky equilibria calculation pdf file makes above remarks concrete.