  Homoclinic and heteroclinic orbits provide a skeleton of the full dynamics of
a chaotic dynamical system and are the foundation of semiclassical sums for
quantum wave packet, coherent state, and transport quantities. Here, the
homoclinic orbits are organized according to the complexity of their
phase-space excursions, and exact relations are derived expressing the relative
classical actions of complicated orbits as linear combinations of those with
simpler excursions plus phase-space cell areas bounded by stable and unstable
manifolds. The total number of homoclinic orbits increases exponentially with
excursion complexity, and the corresponding cell areas decrease exponentially
in size as well. With the specification of a desired precision, the
exponentially proliferating set of homoclinic orbit actions is expressible by a
slower-than-exponentially increasing set of cell areas, which may present a
means for developing greatly simplified semiclassical formulas.
