Potentials unbounded below

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish (US)
Article number042
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume7
DOIs
StatePublished - 2011

Fingerprint

Interpolate
Logistic map
Turning Point
Conjugation
Population Dynamics
Discrete-time
Dynamical system
Lower bound
Motion
Model
Form

Keywords

  • Beverton-holt model
  • Classical dynamical systems
  • Functional conjugation methods
  • Skellam model

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Mathematical Physics

Cite this

Potentials unbounded below. / Curtright, Thomas.

In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 7, 042, 2011.

Research output: Contribution to journalArticle

@article{63352e3347ac4b52b98d340a182d9bd6,
title = "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, 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 = "Beverton-holt model, Classical dynamical systems, Functional conjugation methods, Skellam model",
author = "Thomas Curtright",
year = "2011",
doi = "10.3842/SIGMA.2011.042",
language = "English (US)",
volume = "7",
journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",
issn = "1815-0659",
publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

TY - JOUR

T1 - Potentials unbounded below

AU - Curtright, Thomas

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Beverton-holt model

KW - Classical dynamical systems

KW - Functional conjugation methods

KW - Skellam model

UR - http://www.scopus.com/inward/record.url?scp=82655187061&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=82655187061&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2011.042

DO - 10.3842/SIGMA.2011.042

M3 - Article

AN - SCOPUS:82655187061

VL - 7

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

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

SN - 1815-0659

M1 - 042

ER -