  Fractal basin boundaries provide an important means of characterizing chaotic
systems. We apply these ideas to general relativity, where other properties
such as Lyapunov exponents are difficult to define in an observer independent
manner. Here we discuss the difficulties in describing chaotic systems in
general relativity and investigate the motion of particles in two- and
three-black-hole spacetimes. We show that the dynamics is chaotic by exhibiting
the basins of attraction of the black holes which have fractal boundaries.
Overcoming problems of principle as well as numerical difficulties, we evaluate
Lyapunov exponents numerically and find that some trajectories have a positive
exponent.
