Fixed Winding Number and the Quasiperiodic Route to Chaos in a Convective Fluid

Abstract

We present an experimental observation of the transition to chaos for quasiperiodic routes of fixed winding number. The hydrodynamical system studied is a Rayleigh-Bénard experiment in mercury, in a time-dependent state with one limit cycle. A second oscillator is imposed by an accurrent. We have measured the fractal dimension of the locked regions at the critical curve as well as the scaling properties associated with two different irrational winding numbers, to which the system was tuned. Our results agree with quantitative theoretical predictions based on the circle map.