  A general relation is derived for the action difference between two fixed
points and a phase space area bounded by the irreducible component of a
heteroclinic tangle. The determination of this area can require accurate
calculation of heteroclinic orbits, which are important in a wide range of
dynamical system problems. For very strongly chaotic systems initial deviations
from a true orbit are magnified by a large exponential rate making direct
computational methods fail quickly. Here, a method is developed that avoids
direct calculation of the orbit by making use of the well-known stability
property of the invariant unstable and stable manifolds. Under an
area-preserving map, this property assures that any initial deviation from the
stable (unstable) manifold collapses onto themselves under inverse (forward)
iterations of the map. Using a set of judiciously chosen auxiliary points on
the manifolds, long orbit segments can be calculated using the stable and
unstable manifold intersections of the heteroclinic (homoclinic) tangle.
Detailed calculations using the example of the kicked rotor are provided along
with verification of the relation between action differences. The loop
structure of the heteroclinic tangle is necessarily quite different from that
of the turnstile for a homoclinic tangle, its analogous partner.
