Potentials Unbounded Below
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146859 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Potentials Unbounded Below / T. Curtright // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
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Curtright, T. 2019-02-11T17:24:52Z 2019-02-11T17:24:52Z 2011 Potentials Unbounded Below / T. Curtright // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37C99; 37D45; 37E05; 37J05; 37M99; 39B22 DOI:10.3842/SIGMA.2011.042 https://nasplib.isofts.kiev.ua/handle/123456789/146859 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. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html. I would like to thank the organizers of the workshop on Supersymmetric Quantum Mechanics and Spectral Design, Centro de Ciencias de Benasque Pedro Pascual, for the excellent job they did, and for giving me the opportunity to talk about this work. I also thank Andrzej Veitia and Cosmas Zachos for sharing their thoughts about functional evolution methods, and the anonymous referees for suggestions and questions that led to improvements in the manuscript. Finally, I thank the CERN Theoretical Physics Group for its gracious hospitality and generous support during my sabbatical in 2010. This work was also supported in part by NSF Award 0855386. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Potentials Unbounded Below Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Potentials Unbounded Below |
| spellingShingle |
Potentials Unbounded Below Curtright, T. |
| title_short |
Potentials Unbounded Below |
| title_full |
Potentials Unbounded Below |
| title_fullStr |
Potentials Unbounded Below |
| title_full_unstemmed |
Potentials Unbounded Below |
| title_sort |
potentials unbounded below |
| author |
Curtright, T. |
| author_facet |
Curtright, T. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146859 |
| citation_txt |
Potentials Unbounded Below / T. Curtright // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
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2025-12-07T17:52:17Z |
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2025-12-07T17:52:17Z |
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