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First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator
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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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First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator
Інший ID:
2010 Mathematics Subject Classification: 70H06; 70H33; 53C21
DOI:10.3842/SIGMA.2011.038
DOI:10.3842/SIGMA.2011.038
Посилання:
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.
Підтримка:
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.
Дата:
2011
Переглядів:
538
Завантажень:
294
Анотація:
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.
