Regular and Chaotic Dynamics

, Volume 16, Issue 3–4, pp 223–244 | Cite as

Poisson pencils, algebraic integrability, and separation of variables

Special Issue: Algebraic Integrability


In this paper we 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 discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the bihamiltonian structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice.


Hamilton-Jacobi equations bihamiltonian manifolds separation of variables generalized Toda lattices 

MSC2010 numbers

14H70 37J35 37K10 70H20 


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© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaMilanoItaly
  2. 2.Dipartimento di Ingegneria dell’Informazione e Metodi MatematiciUniversità di BergamoDalmine (BG)Italy

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