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Abstract
We have experimentally studied the transition to chaos in a thermally convecting dilute solution of 3He in superfluid 4He. Two natural oscillatory instabilities are found in our geometry. Mode-locking is observed over a range of Rayleigh and Prandtl number. The mode-locking steps have a measured fractal dimension in good agreement with theoretical predictions and the larger steps show Farey tree ordering. Far below chaos many features of the measurements are suggestive of the circle map. We produce a one-dimensional map showing a tangent bifurcation to a mode-locked state. An effective phase angle change across a mode-locked step is calculated from the data. Close to chaos, hysteresis and other effects are suggestive of a two-dimensional map. The fractal dimension of the attractor is measured over a range of Rayleigh number close to the chaotic onset. Our Poincaré sections show the fractalization of the torus and are characterized by extremely high resolution.
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