BIRKHOFF SIGNATURE CHANGE - A CRITERION FOR THE INSTABILITY OF CHAOTIC RESONANCE

For periodically forced nonlinear oscillators permitting escape from a potential well a relation is observed between two well-known phenomen a, the period-doubling cascade leading to the chaotic escape of the re sonant attractor and the complex dynamics associated with the creation of a structurally unstable homoclinic orbit. The particular homoclini c orbit is identified as that created at the initial change of the per iod one Birkhoff signature of the invariant manifolds of the hilltop s addle. The primary resonant attractor may thus be viewed as the period one simple Newhouse orbit. Significant subharmonic and superharmonic escape events may likewise be associated with nearby Birkhoff signatur e changes. Significant information about the global dynamics may thus be obtained with little numerical effort by inspection of the signatur es of the invariant manifolds of the hilltop saddle.