Abstract

We characterize the three generic quasi-reversible instabilities of closed orbits: the quasi-reversible saddle-node, the Krein collision and the period doubling bifurcation. We show that after a periodic change of variables the asymptotic normal forms of the last two instabilities are the Maxwell-Bloch and the Lorenz equations. We exhibit a simple example of the quasi-reversible period doubling bifurcation, the quasi-reversible 2:1 resonance. © 2001 Elsevier Science B.V.