Suppression of period doubling in the dynamics of a bouncing ball
We present a theoretical and experimental study of a ''bouncing ball'' system, where the effect of a near-resonant perturbation is to suppress the onset of the first period doubling bifurcation. Near the bifurcation point, the full dynamical equations are reduced to a discrete-time map governing the dynamics on a slowly oscillating center manifold. The derivation emphasizes the geometry of the phase-space dynamics, and serves to clarify several points of a recently proposed theory regarding the effects of strong near-resonant perturbations. Our experimental results agree with the simple theory for moderate perturbations; for larger perturbations, higher order effects must be included.
scientific article; zbMATH DE number 3990454