A method for accurate computation of the rotation and the twist numbers of invariant circles

A method is proposed for accurate evaluation of the rotation and the twist numbers of invariant circles in two degrees of freedom Hamiltonian systems or two-dimensional symplectic maps. The method uses the recurrence of orbits to overcome the problems usually arising because of the multivalued character of the angles (due to modulo 2 pi) that have to be added in order to evaluate the above numbers. Furthermore, best convergent demoninators Q(n) of these numbers can be estimated and we show that under a proper treatment of the sequences of Q(n) iterations the accuracy is of the order of 1/Q(n)(4). (C) 2001 Elsevier Science B.V. All rights reserved.