  In this work we develop a method for computing mathematically rigorous
enclosures of some one dimensional manifolds of heteroclinic orbits for
nonlinear maps. Our method exploits a rigorous curve following argument build
on high order Taylor approximation of the local stable/unstable manifolds. The
curve following argument is a uniform interval Newton method applied on short
line segments. The definition of the heteroclinic sets involve compositions of
the map and we use a Lohner-type representation to overcome the accumulation of
roundoff errors. Our argument requires precise control over the local unstable
and stable manifolds so that we must first obtain validated a-posteriori error
bounds on the truncation errors associated with the manifold approximations. We
illustrate the utility of our method by proving some computer assisted theorems
about heteroclinic invariant sets for a volume preserving map of
$\mathbb{R}^3$.
