Gluing bifurcations in critical flows: The route to chaos in parametrically excited surface waves

It is shown that the system of parametrically excited surface waves falls into the class of critical flows whose dynamics and transition to chaos can be understood from first-return maps derived in the vicinity of one saddle point in phase space. The onset of chaos is via gluing bifurcations, which are also common to Lorenz-like flows, but these are intermingled here with usual period-doubling bifurcations. Similar parametrically excited systems might show the full array of routes to chaos which appear in critical flows.