Invariant Sets of Planar Diffeomorphisms in Nonlinear Vibrations

Using the standard technique of Poincaré sampling, many simple periodically forced nonlinear oscillators can be represented by area-contracting planar diffeomorphisms. A class of such diffeomorphisms, referred to as single-sided systems, are considered. These permit escape of orbits to arbitrarily large displacement. Six closure relations which relate the invariant manifolds of the hilltop saddle cycle to other invariant sets are derived. These relations embody much of the underlying organization that is observed in the dynamics of these systems.