First Integrals of Extended Hamiltonians in n+ 1 Dimensions Generated by Powers of an Operator⋆ (original) (raw)

Abstract

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 ...

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  1. The paper presents a method for constructing polynomial first integrals for extended Hamiltonians in n + 1 dimensions.
  2. The extended Hamiltonians are shown to have n + 2 functionally independent first integrals under Liouville integrability conditions.
  3. Constant curvature of the underlying manifold is necessary for constructing additional first integrals U_m(G).
  4. The procedure does not require separability of the Hamiltonian systems, expanding applicability to non-separable cases.
  5. Examples illustrate the construction method for n = 1, 2, and 3, demonstrating superintegrability.

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