- 99-84 Cicogna G., Santoprete M.
- Nonhyperbolic homoclinic chaos
Mar 26, 99
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Abstract. Homoclinic chaos is usually examined with the hypothesis of hyperbolicity
of the critical point. We consider here, following a (suitably adjusted)
classical analytic method, the case of non-hyperbolic points and show
that, under a Melnikov-type condition plus an additional assumption,
the negatively and positively asymptotic sets persist under periodic
perturbations, together with their infinitely many intersections on the
Poincar\'e section. We also examine, by means of essentially the same
procedure, the case of (heteroclinic) orbits tending to the infinity; this
case includes in particular the classical Sitnikov 3--body problem.