Universal behaviour in families of area-preserving maps

@article{Greene1981UniversalBI,
  title={Universal behaviour in families of area-preserving maps},
  author={J. M. Greene and R. MacKay and F. Vivaldi and M. Feigenbaum},
  journal={Physica D: Nonlinear Phenomena},
  year={1981},
  volume={3},
  pages={468-486}
}
We have investigated numerically the behaviour, as a perturbation parameter is varied, of periodic orbits of some reversible area-preserving maps of the plane. Typically, an initially stable periodic orbit loses its stability at some parameter value and gives birth to a stable orbit of twice the period. An infinite sequence of such bifurcations is accomplished in a finite parameter range. This period-doubling sequence has a universal limiting behaviour: the intervals in parameter between… Expand
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