This article is cited in 3 papers

Potentials Unbounded Below

Thomas Curtright<sup>ab

a</sup> CERN, CH-1211 Geneva 23, Switzerland
^b Department of Physics, University of Miami, Coral Gables, FL 33124-8046, USA

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.

Keywords: classical dynamical systems; functional conjugation methods; Beverton–Holt model; Skellam model.

MSC: 37C99; 37D45; 37E05; 37J05; 37M99; 39B22

Received: December 21, 2010; in final form March 27, 2011; Published online April 26, 2011

Language: English

DOI: 10.3842/SIGMA.2011.042

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ArXiv: 1011.6056