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

Abstract

In the context of the theory of symplectic-Haantjes manifolds, we construct the Haantjes structures of generalized Stäckel systems and, as a particular case, of the quasi-bi-Hamiltonian systems. As an application, we recover the Haantjes manifolds for the rational Calogero model with three particles and for the Benenti systems.

We apply the theory of symplectic-Haantjes manifolds introduced in arXiv:1405.5118 (which has been merged with arxiv:1508.04629) to the class of generalized Stäckel systems

References in corpus (3)

• Generalized Lenard Chains, Separation of Variables and Superintegrability
• Recursion Operators and Frobenius Manifolds
• On the characterization of integrable systems via the Haantjes geometry

Cited by in corpus (6)

• Haantjes Algebras and Diagonalization
• An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families
• Haantjes Algebras of the Lagrange Top
• On the Jordan-Chevalley decomposition problem for operator fields in small dimensions and Tempesta-Tondo conjecture
• Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry
• Higher Haantjes Brackets and Integrability