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

We study experimentally the detailed structure of resonances in forced Rayleigh-B\'enard 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.