Analytical and numerical methods are used to study the dynamics in a parameter region away from integrability, where the analytic results of a perturbation analysis of the nearly integrable case are used as a starting point. In the absence of forcing the system is integrable. At any given parameter point we restrict to a bounded subset of phase space, using KAM theory to exclude an infinitely large region with rather trivial dynamics. Our explorations are restricted to large regions of coherent dynamics in phase space and parameter plane. The system is studied in a 1½ degree of freedom Hamiltonian setting with two parameters, where a spatio-temporal symmetry is taken into account. This paper is concerned with the global coherent (i.e., non-chaotic) dynamics of the parametrically forced pendulum.
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December 2022
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