Giorgio Tondo, Piergiulio Tempesta, “Haantjes Structures for the Jacobi–Calogero Model and the Benenti Systems”, SIGMA, 2016, Volume 12,023, 18 pp.

This article is cited in 9 papers

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

Giorgio Tondo^a, Piergiulio Tempesta^bc

^a Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, piaz.le Europa 1, I–34127 Trieste, Italy
^b Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/Nicolás Cabrera, No 13–15, 28049 Madrid, Spain
^c Departamento de Física Teórica II, Facultad de Físicas, Universidad Complutense, 28040 – Madrid, Spain

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.

Keywords: Haantjes tensor; symplectic-Haantjes manifolds; Stäckel systems; quasi-bi-Hamiltonian systems; Benenti systems.

MSC: 37J35; 70H06; 70H20; 53D05

Received: November 3, 2015; in final form February 22, 2016; Published online March 3, 2016

Language: English

DOI: 10.3842/SIGMA.2016.023