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arXiv · 1011.6056

Potentials Unbounded Below

Thomas Curtright
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Abstract

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.

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Thomas Curtright. 2011-04-26. Potentials Unbounded Below. https://doi.org/10.3842/sigma.2011.042

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