On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian

Morosi, Carlo; Tondo, Giorgio

doi:10.1016/s0375-9601(98)00543-x

Cited by 22 publications

(16 citation statements)

References 22 publications

(40 reference statements)

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“…This concept was first introduced in [4] in the particular case of systems with two degrees of freedom and it was quickly extended in [23,24] for a higher-dimensional systems. Some recent papers considering properties of this particular class of systems are [1,2,3,4,5,6,8,14,15,23,24,25,36].…”

Section: Definitionmentioning

confidence: 99%

Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem

Cariñena

Rañada

2016

SIGMA

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Abstract. The existence of quasi-bi-Hamiltonian structures for the Kepler problem is studied. We first relate the superintegrability of the system with the existence of two complex functions endowed with very interesting Poisson bracket properties and then we prove the existence of a quasi-bi-Hamiltonian structure by making use of these two functions. The paper can be considered as divided in two parts. In the first part a quasi-bi-Hamiltonian structure is obtained by making use of polar coordinates and in the second part a new quasi-bi-Hamiltonian structure is obtained by making use of the separability of the system in parabolic coordinates.

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Section: Definitionmentioning

confidence: 99%

Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem

Cariñena

Rañada

2016

SIGMA

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“…In the papers [30,43], it was proved that the Goldfish system (4.5) and the generalized one with Hamiltonian function…”

Section: A Goldf Ish Systemmentioning

confidence: 99%

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

Tondo

Tempesta

2016

SIGMA

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“…A few more comments on the rational case are in order. Firstly, Morosi and Tondo [23] considered a very similar example of separation of variables. Their example is picked out from Calogero's many-body systems describing motion of zeros (or poles) of solutions of a partial differential equation [24].…”

Section: Separation Of Variablesmentioning

confidence: 99%

An integrable system on the moduli space of rational functions and its variants

Takasaki

Takebe

2003

Journal of Geometry and Physics

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We study several integrable Hamiltonian systems on the moduli spaces of meromorphic functions on Riemann surfaces (the Riemann sphere, a cylinder and a torus). The action-angle variables and the separated variables (in Sklyanin's sense) are related via a canonical transformation, the generating function of which is the Abel-Jacobi type integral of the Seiberg-Witten differential over the spectral curve.

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On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian

Cited by 22 publications

References 22 publications

Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem

Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem

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

An integrable system on the moduli space of rational functions and its variants

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