Thermodynamics of the Quasiperiodic Set at the Transition to Chaos: Experimental Results

A periodically driven relaxation oscillator is used to experimentally study the multi-fractal structure of the quasiperiodic set at the transition to chaos. The experimental data provides clear evidence for a phase transition in the thermodynamic free energy q(tau). For positive q, the experimentally measured spectrum of singularities f(alpha) is found to be in good agreement with results from the sine circle map.