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Exact Treatment of a Nonlinear Driven Oscillator

A prototype model of nonlinear driven oscillators with a limit cycle is studied. In the fast-relaxation limit dynamics can be reduced to a one-dimensional mapping. Mode-locking with rational winding numbers takes place for weak external force, while the order of occurence of the orbits is governed by the U-sequence of unimodal mappings for strong external force. In the intermediate region new sequences of periodic orbits occur.