Turbulent inspired experiments and universal statistical patterns in Hamiltonian systems

We discuss some experiments in Hamiltonian systems whose dynamical flow res embles turbulent behavior of fluids. The basic features of the systems asso ciated with this behavior are to be non-integrable and to present critical points of the saddle-center type. Using the technique of histograms for sig nals probed in the flow, we illustrate a road to complete chaos thigh nonin tegrability) as we increase some typical parameters in the system, in a clo se analogy with the road to fully developed turbulence as we increase the R eynolds number. In our analogy, the saddle-center plays the role of a typic al "grid" in experiments with turbulent flows. The central point of this wo rk is that the statistical pattern characterizing high nonintegrability flo w tin analogy with fully developed turbulence) near the saddle-center is un iversal, no matter which Hamiltonian is considered. This statistical distri bution law has the form P(z) proportional to z(-y), with the parameter gamm a related to the chaoticity of the system, indicating the analogy non-chaot ic flow (gamma = 0) or chaotic (turbulent) flow (0 < <gamma> < 1). (C) 2000 Elsevier Science B.V. All rights reserved.