Before revision:  Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior , and to recover the eigenspaces of the endomorphism on homology induced by the self-map.
After revision:  Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior . We establish a sampling theorem to recover the eigenspaces of the endomorphism on homology induced by the self-map.