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In this paper we discuss the relation between the unimodularity of a Liealgebroid $\tau_{A}: A\to Q$ and the existence of invariant volume forms forthe hamiltonian dynamics on the dual bundle $A^{*}$. The results obtained inthis direction are applied to several hamiltonian systems on different examplesof Lie algebroids.

Hamiltonian Dynamics on Lie Algebroids, Unimodularity and Preservation of Volumes