Abstract
A two-dimensional map is derived from the model of a curved Fermi-Pasta-Ulam (FPU) chain which supports exact discrete breather (DB) solutions with frequencies lying outside the linear spectrum or phonon band. The stability of the equilibrium points of the two-dimensional map is examined and the nature of the trajectories is numerically studied. The map displays regular orbits and commensurate states in the phase space for different choices of curvature strength of the FPU chain. The homoclinic map orbits are attributed to the stationary DB solutions of the lattice system.
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