Braids on the Poincaré section: A laser example

We discuss the topological analysis of dynamical systems represented by two-dimensional maps emphasizing the case of Poincaré maps. The central 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 braid types associated with periodic orbits (up to a global torsion). Since some braids imply positive topological entropy, the topological analysis can be regarded as a test of chaos. The method is specially suited 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 the reconstruction of the phase space of the flow is nearly impossible. © 1996 The American Physical Society.