On a Paper of G. Iooss

Abstract

This paper [3] proves the existence of the Hopf bifurcation to a periodic solution from a stationary solution in certain problems of fluid dynamics. The results are similar to those already described. For instance, in the subcritical case, the periodic solution is shown to be unstable in the sense of Lyapunov when the real bifurcation parameter (Reynold’s number) is less than the critical value where the bifurcation takes place; it is shown to be (exponentially) stable if this value is greater than the critical value in the supercritical case.