K. Efstathiou et N. Voglis, A method for accurate computation of the rotation and the twist numbers ofinvariant circles, PHYSICA D, 158(1-4), 2001, pp. 151-163
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 orbit
s to overcome the problems usually arising because of the multivalued chara
cter of the angles (due to modulo 2 pi) that have to be added in order to e
valuate the above numbers. Furthermore, best convergent demoninators Q(n) o
f 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.