Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 042, 20 pages      arXiv:1011.6056      https://doi.org/10.3842/SIGMA.2011.042
Contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design”

Potentials Unbounded Below

Thomas Curtright a, b
a) CERN, CH-1211 Geneva 23, Switzerland
b) Department of Physics, University of Miami, Coral Gables, FL 33124-8046, USA

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

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.

Key words: classical dynamical systems; functional conjugation methods; Beverton-Holt model; Skellam model.

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