On homoclinic splitting problems

Counterexamples to the homoclinic splitting claimed in the paper “Existence of exponentially small separatrix settings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems” by Rudnev and Wiggins [Physica D 114 (1998) 3–80] are given. These counterexamples invalidate the proofs of the main results of that paper.