The Dynamics of Regularized Discontinuous Maps with Applications to Impacting Systems

@article{Pring2010TheDO,
  title={The Dynamics of Regularized Discontinuous Maps with Applications to Impacting Systems},
  author={S. R. Pring and Chris J. Budd},
  journal={SIAM J. Appl. Dyn. Syst.},
  year={2010},
  volume={9},
  pages={188-219}
}
One-dimensional piecewise-smooth discontinuous maps (maps with gaps) are known to have surprisingly rich dynamics, including periodic orbits with very high period and bifurcation diagrams showing period-adding or period-incrementing behavior. In this paper we study a new class of maps, which we refer to as regularized one-dimensional discontinuous maps, because they give very similar dynamics to discontinuous maps and closely approximate them, yet are continuous. We show that regularized… 

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