Nonhyperbolic homoclinic chaos

Homoclinic chaos is usually examined with the hypothesis of hyperbolicity o f the critical point. We consider here, following a (suitably adjusted) cla ssical analytic method, the case of non-hyperbolic points and show that, un der a Melnikov-type condition plus an additional assumption, the negatively and positively asymptotic sets persist under periodic perturbations, toget her with their infinitely many intersections on the Poincare section. We al so examine, by means of essentially the same procedure, the case of (hetero clinic) orbits tending to the infinity; this case includes in particular th e classical Sitnikov 3-body problem. (C) 1999 Elsevier Science B.V. Ail rig hts reserved.