Taylor-Chirikov map package: A package of programs for the calculation of ordered periodic orbits of area preserving twist maps. 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.

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