Haantjes Structures for the Jacobi-Calogero Model and the Benenti Systems.
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2016
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NATL ACAD SCI UKRAINE, INST MATH
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Abstract
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 an application, we recover the Haantjes manifolds for the rational Calogero model with three particles and for the Benenti systems.
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© NATL ACAD SCI UKRAINE, INST MATH.
The work of P.T. has been partly supported by the research project FIS2015-63966, MINECO, Spain and partly by ICMAT Severo Ochoa project SEV-2015-0554 (MINECO). G.T. acknowledges the financial support of the research project PRIN 2010-11 \Geometric and analytic theory of Hamiltonian systems in finite and infinite dimensions". Moreover, he thanks G. Rastelli for interesting discussions about the Jacobi{Calogero model. We also thank the anonymous referees for a careful reading of the manuscript and for several useful suggestions.