Quasi-reversible instabilities of closed orbits

We characterize the three generic quasi-reversible instabilities of closed orbits: the quasi-reversible saddle-node, the Krein collision and the perio d doubling bifurcation. We show that after a periodic change of variables t he asymptotic normal forms of the last two instabilities are the Maxwell-Bl och and the Lorenz equations. We exhibit a simple example of the quasi-reve rsible period doubling bifurcation, the quasi-reversible 2:1 resonance. (C) 2001 Elsevier Science B.V. All rights reserved.