Potentials Unbounded Below
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, . Typically, has no lower bound and can exhibit switchbacks wherein 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.
Cite
@article{arxiv.1011.6056,
title = {Potentials Unbounded Below},
author = {Thomas Curtright},
journal= {arXiv preprint arXiv:1011.6056},
year = {2011}
}
Comments
Based on a talk given 29 July 2010, at the workshop on Supersymmetric Quantum Mechanics and Spectral Design, Centro de Ciencias de Benasque Pedro Pascual. This version incorporates modifications to conform to the published paper: Additional references and discussion; New section 3.2 on the Skellam exponential model; Appendix changed