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

K. Efstathiou, N. Voglis

Physica D, 158(1-4), 151-163 (2001)
10.1016/S0167-2789(01)00299-8
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Abstract

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 $1/Q_n^4$.