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Manuscript Title: Taylor-Chirikov map package: a package of programs for the calculation of ordered periodic orbits of area preserving twist maps.
Authors: Q. Chen, B.D. Mestel
Catalogue identifier: ABBW_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 51(1988)463
Programming language: Fortran.
Computer: ICL 2988.
Operating system: VME 8.16.
RAM: 4K words
Word size: 32
Keywords: Hamiltonian, Taylor-chirikov map, Non-linear dynamics, Orbits, Newton method, Plasma physics, Particle physics, Elementary, Accelerators, Collisionless plasma.
Classification: 11.10, 19.3.

Nature of problem:
The study of area preserving twist maps of the plane is important for many fields of physics including Hamiltonian dynamics, plasma confinement, particle accelerator design and condensed matter physics. This is a package of programs to facilitate the calculation of ordered periodic orbits of these maps, particularly in the presence of large nonlinearities.

Solution method:
The problem is formulated in variational terms and a Newton algorithm is used to calculate the orbits. Good initial conditions for the Newton scheme are obtained by a number of techniques based on the limiting cases of zero and infinite nonlinearity, averaging of the orbits for zero nonlinearity and for the so-called sawtooth map, and using the bunching of orbits together with the continued fraction expansion of the frequency.

The package is limited to the special class of area preserving twist maps of the plane known as the Taylor-Chirikov type maps. While the package may be used to find some badly ordered orbits, its primary use is for the calculation of ordered periodic orbits.

Unusual features:

Running time:
The running time is O(n) where n is the period of the orbits to be calculated. The compile-load-go run of the test program took 17s of processor time running interactively under the VME 8.16 operating system on the ICL 2988 computer at Queen Mary College.