If one changes the control parameter of a chaotic system proportionall
y to the distance between an arbitrary point on the strange attractor
and the actual trajectory, the lifetime tau of the most stable unstabl
e periodic orbit in the vicinity of this point starts to diverge with
a power law. The volume in parameter space where tau becomes infinite
is finite and from its nonfractal boundaries one can determine directl
y the local Liapunov exponents. The experimental applicability of the
method is demonstrated for two coupled diode resonators.