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arXiv · 2504.02189

Solvable Structures for Hamiltonian Systems

Sasa Kresic-Juric·Concepcion Muriel·Adrian Ruiz
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Abstract

In this paper, we investigate solvable structures associated to Hamiltonian equations. For a completely integrable Hamiltonian system with $n$ degrees of freedom, we construct a canonical solvable structure consisting of $2n$ Hamiltonian vector fields. We derive explicit expressions for the corresponding Pfaffian forms, whose integration provides solutions to the Hamiltonian equations. We show that the upper $n$ forms give the action varibles, while the lower $n$ forms yield the angle variables of the system. This offers a novel interpretation of the Arnold--Liouville theorem in terms of solvable structures. We ilustrate the theory by deriving explicit solutions and action--angle variables for $n$ harmonic oscillators and the Calogero--Moser system.

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Sasa Kresic-Juric, Concepcion Muriel, Adrian Ruiz. 2025-04-03. Solvable Structures for Hamiltonian Systems. https://arxiv.org/abs/2504.02189

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