First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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dc.contributor.author	Chanu, C.
dc.contributor.author	Degiovanni, L.
dc.contributor.author	Rastelli, G.
dc.date.accessioned	2019-02-11T17:17:50Z
dc.date.available	2019-02-11T17:17:50Z
dc.date.issued	2011
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 70H06; 70H33; 53C21
dc.identifier.other	DOI:10.3842/SIGMA.2011.038
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/146855
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA