Potentials Unbounded Below

Details Potentials Unbounded Below Potentials Unbounded Below

2010-11-28

arxiv.org/abs/1011.6056v3

SIGMA 7:042,2011

Physics

Mathematical Physics

Based on a talk given 29 July 2010, at the workshop on Supersymmetric Quantum Mechanics and Spectral Design, Centro de Ciencia

Scientific paper

10.3842/SIGMA.2011.042

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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