# On the characterization of integrable systems via the Haantjes geometry

@article{Tempesta2015OnTC, title={On the characterization of integrable systems via the Haantjes geometry}, author={P. Tempesta and G. Tondo}, journal={arXiv: Mathematical Physics}, year={2015} }

We prove that the existence of a Haantjes structure is a necessary and sufficient condition for a Hamiltonian system to be integrable in the Liouville-Arnold sense. This structure, expressed in terms of suitable operators whose Haantjes torsion vanishes, encodes the main features of the notion of integrability, and in particular, under certain hypotheses, allows to solve the problem of determining separation of variables for a given system in an algorithmic way.
As an application of the theory… Expand

#### One Citation

Haantjes Structures for the Jacobi-Calogero Model and the Benenti Systems

- Mathematics, Physics
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In the context of the theory of symplectic-Haantjes manifolds, we construct the Haantjes structures of generalized Stackel systems and, as a particular case, of the quasi-bi-Hamiltonian systems. As… Expand

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