Critical exponent of chaotic transients in nonlinear dynamical systems.

The average lifetime of a chaotic transient versus a system parameter is studied for the case wherein a chaotic attractor is converted into a chaotic transient upon collision with its basin boundary (a crisis). Typically the a~erage lifetime T depends upon the system parameter p via T —~p —p, ~ &, where p, denotes the value of p at the crisis and we caII y the critical exponent of the chaotic transient. A theory determining y for two-dimensional maps is developed and compared ~ith numerical experiments. The theory also applies to critical behavior at interior crises.