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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• Main Authors: Chanu, C., Degiovanni, L., Rastelli, G.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146855
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...