Simultaneous dense and nondense orbits for noncommuting toral endomorphisms

Let S and T be hyperbolic endomorphisms of with the property that the span of the subspace contracted by S along with the subspace contracted by T is . We show that the intersection of the set of points with equidistributing orbit under S with the set of points with nondense orbit under T has maximal Hausdorff dimension. In the case that S and T are quasihyperbolic automorphisms, we prove that the Hausdorff dimension of the intersection is again maximal when we assume that is spanned by the subspaces contracted by S and T along with the central eigenspaces of S and T.