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• W2265839730 abstract "A general theory of classical integrable systems is proposed, based on the geometry of the Haantjes tensor. We introduce the class of symplectic-Haantjes manifolds (or $omega mathcal{H}$ manifold), as the natural setting where the notion of integrability can be formulated. We prove that the existence of suitable Haantjes structures is a necessary and sufficient condition for a Hamiltonian system to be integrable in the Liouville-Arnold sense. We also prove theorems ensuring the existence of a large family of completely integrable systems, constructed starting from a prescribed Haantjes structure. Furthermore, we propose a novel approach to the theory of separation of variables, intimately related to the geometry of Haantjes manifolds. A special family of coordinates, that we shall call the Darboux-Haantjes coordinates, will be introduced. They are constructed from the Haantjes structure associated with an integrable system, and allow the additive separation of variables of the Hamilton-Jacobi equation. Our analysis is performed in $n$ degrees of freedom. We prove that some of the most classical examples of multidimensional Hamiltonian systems, as for instance the Gantmacher class, possess a natural Haantjes structure. Finally, we present an application of our approach to the study of some models, as a stationary reduction of the KdV hierarchy and a Drach-Holt type system; the separability properties of the latter were not known." @default.
• W2265839730 created "2016-06-24" @default.
• W2265839730 creator A5038563250 @default.
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• W2265839730 date "2014-05-20" @default.
• W2265839730 modified "2023-09-27" @default.
• W2265839730 title "Haantjes Manifolds of Classical Integrable Systems" @default.
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