  Chaotic dynamics can be effectively studied by continuation from an
anti-integrable limit. We use this limit to assign global symbols to orbits and
use continuation from the limit to study their bifurcations. We find a bound on
the parameter range for which the Henon map exhibits a complete binary
horseshoe as well as a subshift of finite type. We classify homoclinic
bifurcations, and study those for the area preserving case in detail. Simple
forcing relations between homoclinic orbits are established. We show that a
symmetry of the map gives rise to constraints on certain sequences of
homoclinic bifurcations. Our numerical studies also identify the bifurcations
that bound intervals on which the topological entropy is apparently constant.
