  Black holes binaries support unstable orbits at very close separations. In
the simplest case of geodesics around a Schwarzschild black hole the orbits,
though unstable, are regular. Under perturbation the unstable orbits can become
the locus of chaos. All unstable orbits, whether regular or chaotic, can be
quantified by their Lyapunov exponents. The exponents are observationally
relevant since the phase of gravitational waves can decohere in a Lyapunov
time. If the timescale for dissipation due to gravitational waves is shorter
than the Lyapunov time, chaos will be damped and essentially unobservable. We
find the timescales can be comparable. We emphasize that the Lyapunov exponents
must only be used cautiously for several reasons: they are relative and depend
on the coordinate system used, they vary from orbit to orbit, and finally they
can be deceptively diluted by transient behaviour for orbits which pass in and
out of unstable regions.
