Structure of Arnold tongues and the f(α) spectrum for period doubling: Experimental results

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Abstract
We study experimentally the detailed structure of resonances in forced Rayleigh-Bénard convection in mercury. The resonances appear as Arnold tongues in the phase diagram of the system. We follow a particular tongue beyond the critical line where tongues start to overlap and find a period-doubling curve stretching over the entire tongue. Above this line there is a symmetry breaking with period-doubling cascades at the two sides of the tongue. We also observe a multitude of other periodic windows in this regime together with hysteresis effects caused by overlap of other tongues. We follow one of the period-doubling cascades and study the full scaling structure of the attractor at the onset of chaos by means of an f(α) spectrum of scaling indices. The experimental spectrum is, within error, the same as the universal spectrum calculated theoretically.