Global periodic structure of integrable Duffing’s maps

Integrable Duffing’s mappings have been constructed on the basis of a scheme presented by Suris. The Poincaré–Birkhoff resonance condition determines the periodic behavior of the orbit close to the fixed points of the integrable mappings. In the region far apart from the fixed points, the nonlinear effect modifies the property of the periodic orbits. Here, the global behavior of periodic orbits of the integrable Duffing’s maps is investigated by applying the Fourier analysis on the individual orbits.