BRAIDS ON THE POINCARE SECTION - A LASER EXAMPLE

We discuss the topological analysis of dynamical systems represented b y two-dimensional maps emphasizing the case of Poincare maps. The cent ral result consists in the implementation of a recent presentation of braids as deformations of circles [M. A. Natiello and H. G. Solari, J. Knot Theory Ramifications 3, 511 (1994)] to the determination of brai d types associated with periodic orbits (up to a global torsion). Sinc e some braids imply positive topological entropy, the topological anal ysis can be regarded as a test of chaos. The method is specially suite d for experiments where the complete reconstruction of the phase space for the flow cannot be achieved at a reasonable cost. We apply these ideas to data sets produced in a laser physics experiment for which th e reconstruction of the phase space of the flow is nearly impossible.