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Manuscript Title: Poincare sections of Hamiltonian systems.
Authors: E.S. Cheb-Terrab, H.P. de Oliveira
Program title: Poincare
Catalogue identifier: ADDC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 95(1996)171
Programming language: Maple.
Computer: Pentium-90 PC.
Operating system: UNIX, DOS, DEC VMS, IBM CMS.
RAM: 8M words
Keywords: Computer algebra, Graphics, Hamiltonian systems, Surface-of-section, Method, Symbolic computing.
Classification: 5, 14.

Nature of problem:
Computation and plotting of 2D/3D projections of Poincare surfaces-of- section of Hamiltonian systems.

Solution method:
A 4th order Runge-Kutta method with optional stepsize and number of iterations is used. However, it is possible to indicate any user-method to be used in the integration scheme.

Restrictions:
Besides the inherent restrictions of the Runge-Kutta method, this first version of the package does not make use of adaptative stepsize control.

Unusual features:
This package provides easy-to-use software tools for plottings 2D/3D projections of Poincare surfaces-of-section of Hamiltonians systems. The speed at which the returned plots are calculated is adjustable, in connection with their accuracy. This feature permits alternatively searching for, say, "first order" phenomena at remarkable high speed, or, say, "high order" detailed 2D/3D projections displaying "islands" and the inner structure of a surface-of-section, as desired. The 2D intersection plane over which the surface-of-section is plotted can be any one of the coordinate planes of the phase space, and can be shifted in the positive and negative directions. The package also provides routines for setting large sets of initial conditions for numerical experiments in seconds. The implementation in a symbolic computing environment allows for combined symbolic/numerical studies.

Running time:
It depends strongly on the surface-of-section to be plotted. With a Pentium-90 PC (32 Mb. RAM), fast plots usually take from a few seconds to a few minutes. On the other extreme, in an example considered in this paper, a surface-of-section with 10,000 points and an energy threshold approx 10**-8 took 35 minutes.