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 language | English (US) |
|---|---|
| Article number | 042 |
| Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
| Volume | 7 |
| DOIs | |
| State | Published - 2011 |
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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 journal › Article
}
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 -