Combining Topological Analysis and Symbolic Dynamics to Describe a Strange Attractor and Its Crises

We show how to use topological analysis to construct from experimental data a symbolic coding of a chaotic attractor. Time series data from a chaotic ${\mathrm{CO}}_2$ laser with modulated losses operating within parameter regions corresponding to attractor crises have been analyzed. A procedure for determining a generating partition from the data is presented, and the connection between crises and a symbolic description of the dynamics is determined.