Hamiltonian Dynamics on Lie Algebroids, Unimodularity and Preservation of Volumes

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 $A^{\ast }$. The results obtained in this direction are applied to several hamiltonian systems on different examples of Lie algebroids.

16 pages

References in corpus (1)

• On the Integration Theory of Equations of Nonholonomic Mechanics

Cited by in corpus (1)

• Quantum Systems as Lie Algebroids