Juan Carlos Marrero (Uiversidad de La Laguna, Tenerife)

Hamiltonian dynamics on Lie algebroids, unimodularity and preservation of volumes

The modular class of a Lie algebroid A was introduced by Evens, Lu and Weinstein (Quart. J. Math. Oxford 50, (1999), 417-436) as a cohomology class of order 1 in the Lie algebroid cohomology of A with trivial coefficients. A is said to be unimodular if its modular class is zero. In this talk, I will present some recent results about the relation between the unimodularity of A and the existence of invariant volume forms for a hamiltonian system on the dual bundle A_ to A. Applications of these results to several Poisson mechanical systems will be also given.