UNSTABLE FIXED-POINTS, HETEROCLINIC CYCLES AND EXPONENTIAL TAILS IN TURBULENCE PRODUCTION

We show that solutions of ordinary differential equations possessing attracting heteroclinic cycles and subject to small random or periodic perturbations typically exhibit sharp events whose separations are well characterized by a probability distribution with an exponential tail. We review experimental evidence for such distributions in turbulent flows and indicate how our simple theory might be used to identify instability mechanisms.