First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator
We describe a procedure to construct polynomial in the momenta first integrals of arbitrarily high degree for natural Hamiltonians H obtained as one-dimensional extensions of natural (geodesic) n-dimensional Hamiltonians L. The Liouville integrability of L implies the (minimal) superintegrability of...
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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/123456789/146855 |
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| Zitieren: | First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator / C. Chanu, L. Degiovanni, G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. |
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Chanu, C. Degiovanni, L. Rastelli, G. 2019-02-11T17:17:50Z 2019-02-11T17:17:50Z 2011 First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator / C. Chanu, L. Degiovanni, G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70H06; 70H33; 53C21 DOI:10.3842/SIGMA.2011.038 https://nasplib.isofts.kiev.ua/handle/123456789/146855 We describe a procedure to construct polynomial in the momenta first integrals of arbitrarily high degree for natural Hamiltonians H obtained as one-dimensional extensions of natural (geodesic) n-dimensional Hamiltonians L. The Liouville integrability of L implies the (minimal) superintegrability of H. We prove that, as a consequence of natural integrability conditions, it is necessary for the construction that the curvature of the metric tensor associated with L is constant. As examples, the procedure is applied to one-dimensional L, including and improving earlier results, and to two and three-dimensional L, providing new superintegrable systems. This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S4)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html. The research has been partially supported (C.C.) by the European program “Dote ricercatori” (F.S.E. and Regione Lombardia). G.R. is particularly grateful to the University of Waterloo, ON, Canada, where part of the research has been done during a visit. The authors wish to thank F. Magri and R.G. McLenaghan for their suggestions and stimulating discussions about the topic of the present research. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator |
| spellingShingle |
First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator Chanu, C. Degiovanni, L. Rastelli, G. |
| title_short |
First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator |
| title_full |
First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator |
| title_fullStr |
First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator |
| title_full_unstemmed |
First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator |
| title_sort |
first integrals of extended hamiltonians in n+1 dimensions generated by powers of an operator |
| author |
Chanu, C. Degiovanni, L. Rastelli, G. |
| author_facet |
Chanu, C. Degiovanni, L. Rastelli, G. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We describe a procedure to construct polynomial in the momenta first integrals of arbitrarily high degree for natural Hamiltonians H obtained as one-dimensional extensions of natural (geodesic) n-dimensional Hamiltonians L. The Liouville integrability of L implies the (minimal) superintegrability of H. We prove that, as a consequence of natural integrability conditions, it is necessary for the construction that the curvature of the metric tensor associated with L is constant. As examples, the procedure is applied to one-dimensional L, including and improving earlier results, and to two and three-dimensional L, providing new superintegrable systems.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146855 |
| citation_txt |
First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator / C. Chanu, L. Degiovanni, G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. |
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2025-12-07T15:42:21Z |
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2025-12-07T15:42:21Z |
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