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2-D Duffing oscillator: elliptic functions from a dynamical systems point of view. (English) Zbl 1270.33011
Qual. Theory Dyn. Syst. 12, No. 1, 115-139 (2013); erratum ibid. 12, No. 1, 141–142 (2013).
Summary: K. R. Meyer [Am. Math. Mon. 108, No. 8, 729–737 (2001; Zbl 1129.33315)] has advocated for the study of elliptic functions and integrals from a dynamical systems point of view. Here, we follow his advice and we propose the bidimensional Hamiltonian Duffing oscillator as a model; it allows us to deal with the elliptic integral of third kind directly. Focusing on bounded trajectories we do a detailed analysis of the solutions in the three regions defined by the parameters. In our opinion, for the study of elliptic functions, the model presented here represents an alternative to the pendulum or the free rigid body systems.

MSC:
33E05 Elliptic functions and integrals
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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