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Hamiltonian Dynamics on Lie Algebroids, Unimodularity and Preservation of Volumes
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abstract
In this paper we discuss the relation between the unimodularity of a Lie algebroid $\tau_{A}: A\to Q$ and the existence of invariant volume forms for the hamiltonian dynamics on the dual bundle $A^{*}$. The results obtained in this direction are applied to several hamiltonian systems on different examples of Lie algebroids.
Forward citations
Cited by 2 Pith papers
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Optimal control problems on the co-adjoint Lie groupoids
Any right-invariant optimal control problem on a Lie groupoid is claimed to reduce to one on its co-adjoint Lie algebroid, but the key step is cited, not proven.
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A note on integrabiliy of Hamiltonian systems on the co-adjoint Lie groupoids
On co-adjoint Lie groupoids of product form, Hamiltonian integrability is claimed to reduce to the integrability of a Hamiltonian system on a co-adjoint orbit, but the derivation is not sound.
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