HAMILTONIAN MECHANICAL SYSTEMS ON LIE ALGEBROIDS, UNIMODULARITY AND PRESERVATION OF VOLUMES

作者：Carlos Marrero Juan

来源：Journal of Geometric Mechanics, 2010, 2(3): 243-263.

DOI：10.3934/jgm.2010.2.243

• Lie algebroids
• linear Poisson structure
• Hamiltonian mechanical systems
• modular class
• unimodularity
• volume forms

In this paper we discuss the relation between the unimodularity of a Lie algebroid tau(A) : A --> Q and the existence of invariant volume forms for the dynamics of hamiltonian mechanical systems on the dual bundle A*. The results obtained in this direction are applied to several hamiltonian systems on different examples of Lie algebroids.

• 出版日期2010-9