Poincarè versus Boltzmann in Shil'nikov phenomena

By suitable adjustment of the control parameters in a CO2 laser with feedback we show experimental evidence of Sil'nikov chaos, characterized by intensity pulses almost equal in shape, but irregularly separated in time. The times of return to a Poincare section are statistically spread, however their iteration map is one-dimensional and in close agreement with that arising from Sil'nikov theory. Thus, the iteration map of the time intervals becomes the most appropriate indicator of this chaos. The residual width of the experimentally measured maps is due to a transient fluctuation enhancement peculiar to macroscopic systems, which is absent in low-dimensional chaotic dynamics. This appears as an inestricable mixture of deterministic unpredictability as introduced by Poincare and stochastic fluctuations as considered in Boltzmann statistical mechanics.