Abstract
SIGMA 7:042,2011 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.
