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arXiv · 2401.04673

Algebraic curves as a source of separable multi-Hamiltonian systems

Maciej Blaszak·Krzysztof Marciniak
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Abstract

In this paper we systematically consider various ways of generating integrable and separable Hamiltonian systems in canonical and in non-canonical representations from algebraic curves on the plane. In particular, we consider St\"ackel transform between two pairs of St\"ackel systems, generated by 2n-parameter algebraic curves on the plane, as well as Miura maps between St\"ackel systems generated by (n+N)-parameter algebraic curves, leading to multi-Hamiltonian representation of these systems.

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Maciej Blaszak, Krzysztof Marciniak. 2024-01-09. Algebraic curves as a source of separable multi-Hamiltonian systems. https://doi.org/10.46298/ocnmp.12861

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