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

K. Efstathiou, N. Voglis (2001)
Physica D

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 $2 π$ ) 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 $1 / Q_{n}^{4}$ .

@article{2001_EV_Accurate_Rotation_Number,
 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 $2π$) 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 $1/Q_n^4$.},
 author = {Efstathiou, K. and Voglis, N.},
 doi = {10.1016/S0167-2789(01)00299-8},
 journal = {Physica D},
 journalurl = {https://www.elsevier.com/locate/physd},
 number = {1-4},
 pages = {151-163},
 title = {A method for accurate computation of the rotation and the twist numbers of invariant circles},
 volume = {158},
 year = {2001}
}