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arXiv · 2411.19815

Superintegrability and geometry: a review of the extended Hamiltonian approach

Claudia Maria Chanu·Giovanni Rastelli
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Abstract

We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of arbitrarily high degree. In particular, we focus on the geometric structures involved by the procedure: warped manifolds and Riemannian coverings. Examples of superintegrable systems, classical and quantum, with the structure of extended Hamiltonians are anisotropic harmonic oscillators, Kepler-Coulomb, Tremblay-Turbiner-Winternitz and Post-Winternitz systems.

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Claudia Maria Chanu, Giovanni Rastelli. 2024-11-29. Superintegrability and geometry: a review of the extended Hamiltonian approach. https://arxiv.org/abs/2411.19815

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