Taylor-Chirikov map swMATH ID: 11186 Software Authors: Chen, Qi Keith; Mestel, B.D. Description: 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. Homepage: http://cpc.cs.qub.ac.uk/summaries/ABBW_v1_0.html Keywords: Taylor-Chirikov map package; Hamiltonian; nonlinear dynamics; orbits; Newton method Related Software: Cited in: 4 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Taylor-Chirikov map package: A package of programs for the calculation of ordered periodic orbits of area preserving twist maps. Zbl 0812.65063Chen, Qi Keith; Mestel, B. D. 1988 all top 5 Cited by 6 Authors 1 Chen, Qi Keith 1 Chen, Qi 1 Dana, Itzhack 1 Meiss, James D. 1 Murray, N. W. 1 Percival, Ian C. Cited in 2 Serials 3 Physica D 1 Computer Physics Communications all top 5 Cited in 6 Fields 4 Dynamical systems and ergodic theory (37-XX) 2 Mechanics of particles and systems (70-XX) 1 Ordinary differential equations (34-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) Citations by Year