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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
National Academy of Science of Ukraine
2011-04-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2011.038 |
| _version_ | 1818765794073378816 |
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| author | Giovanni Rastelli Luca Degiovanni Claudia Chanu |
| author_facet | Giovanni Rastelli Luca Degiovanni Claudia Chanu |
| author_sort | Giovanni Rastelli |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-18T08:23:45Z |
| format | Article |
| id | doaj.art-cdd1630953634d4da9900f04d2d4d5d6 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-18T08:23:45Z |
| publishDate | 2011-04-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-cdd1630953634d4da9900f04d2d4d5d62022-12-21T21:14:40ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592011-04-017038First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an OperatorGiovanni RastelliLuca DegiovanniClaudia ChanuWe 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.http://dx.doi.org/10.3842/SIGMA.2011.038superintegrable Hamiltonian systemspolynomial first integralsconstant curvatureHessian tensor |
| spellingShingle | Giovanni Rastelli Luca Degiovanni Claudia Chanu First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator Symmetry, Integrability and Geometry: Methods and Applications superintegrable Hamiltonian systems polynomial first integrals constant curvature Hessian tensor |
| title | 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_short | 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 |
| topic | superintegrable Hamiltonian systems polynomial first integrals constant curvature Hessian tensor |
| url | http://dx.doi.org/10.3842/SIGMA.2011.038 |
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