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.

Degiovanni, L., Rastelli, G., Chanu, C. (2011). First integrals of extended Hamiltonians in (n+1)-dimensions generated by powers of an operator. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 7, 038 [10.3842/SIGMA.2011.038].

First integrals of extended Hamiltonians in (n+1)-dimensions generated by powers of an operator

CHANU, CLAUDIA MARIA
2011

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.
Articolo in rivista - Articolo scientifico
superintegrable systems
English
2011
7
038
038
none
Degiovanni, L., Rastelli, G., Chanu, C. (2011). First integrals of extended Hamiltonians in (n+1)-dimensions generated by powers of an operator. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 7, 038 [10.3842/SIGMA.2011.038].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/21516
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