Potentials unbounded below

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3 Scopus citations


Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The interpolates correspond to particle motion in an underlying potential, V. Typically, V has no lower bound and can exhibit switchbacks wherein V changes form when turning points are encountered by the particle. The Beverton-Holt and Skellam models of population dynamics, and particular cases of the logistic map are used to illustrate these features.

Original languageEnglish (US)
Article number042
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
StatePublished - 2011


  • Beverton-holt model
  • Classical dynamical systems
  • Functional conjugation methods
  • Skellam model

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology


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