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

TL;DR

This paper constructs Haantjes structures for generalized Stäckel and quasi-bi-Hamiltonian systems, applying them to recover structures for the Calogero model and Benenti systems, advancing geometric understanding of integrable models.

Contribution

It introduces Haantjes structures for a broad class of integrable systems, including Stäckel and Benenti systems, unifying geometric frameworks for these models.

Findings

Haantjes structures constructed for generalized Stäckel systems

Recovered Haantjes manifolds for the rational Calogero model

Established Haantjes structures for Benenti systems

Abstract

In the context of the theory of symplectic-Haantjes manifolds, we construct the Haantjes structures of generalized St\"ackel 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.