STABILITY OF MINIMAL PERIODIC-ORBITS

Symplectic twist maps are obtained from a Lagrangian variational princ iple. It is well known that nondegenerate minima of the action corresp ond to hyperbolic orbits of the map when the twist is negative definit e and the map is two-dimensional, We show that for more than two dimen sions, periodic orbits with minimal action in symplectic twist maps wi th negative definite twist are not necessarily hyperbolic. In the proo f we show that in the neighborhood of a minimal periodic orbit of peri od n, the nth iterate of the map is again a twist map. This is true ev en though in general the composition of twist maps is not a twist map. (C) 1998 Elsevier Science B.V.