  Fluctuational transitions between two co-existing chaotic attractors,
separated by a fractal basin boundary, are studied in a discrete dynamical
system. It is shown that the mechanism for such transitions is determined by a
hierarchy of homoclinic points. The most probable escape path from the chaotic
attractor to the fractal boundary is found using both statistical analyses of
fluctuational trajectories and the Hamiltonian theory of fluctuations.
