Hamiltonian Dynamics on Lie Algebroids, Unimodularity and Preservation of Volumes
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.