TITLE: Singular splitting of separatrices for the perturbed McMillan map AUTHORS: Amadeu Delshams, Rafael Ramirez-Ros Departament de Matematica Aplicada I Universitat Politecnica de Catalunya Diagonal 647, 08028 Barcelona, Spain E-mails: amadeu@ma1.upc.es, rafael@tere.upc.es ABSTRACT: In this communication we review the difficult analytical and numerical problems that arise in the computation of the exponentially small splitting of separatrices of a general twist perturbation of the McMillan map. KEYWORDS: Area-preserving map, singular separatrix splitting, Melnikov method, numerical experiments MSC numbers: 34C37, 34E05, 34E15, 65L12