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 2π) that have to be added in order to evaluate the above numbers. Furthermore, best convergent demoninators Qn of these numbers can be estimated and we show that under a proper treatment of the sequences of Qn iterations the accuracy is of the order of 1/Qn4.