00961nas a2200109   4500008004300000245006400043210006200107260001000169520061500179100002100794856003600815       2003                        en_Ud  00aPoisson Pencils, Integrability, and Separation of Variables0 aPoisson Pencils Integrability and Separation of Variables  bSISSA3 aIn this paper we will review a recently introduced method for solving the Hamilton-Jacobi equations by the method of Separation of Variables. This method is based on the notion of pencil of Poisson brackets and on the bihamiltonian approach to integrable systems. We will discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the \\\\bih structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice.1 aFalqui, Gregorio  uhttp://hdl.handle.net/1963/3026