00848nas a2200109   4500008004300000245006600043210006600109260001900175520048700194100002100681856003600702       2001                        en_Ud  00aLax representation and Poisson geometry of the Kowalevski top0 aLax representation and Poisson geometry of the Kowalevski top  bIOP Publishing3 aWe discuss the Poisson structure underlying the two-field Kowalevski gyrostat and the Kowalevski top. We start from their Lax structure and construct a suitable pencil of Poisson brackets which endows these systems with the structure of bi-Hamiltonian completely integrable systems. We study the Casimir functions of such pencils, and show how it is possible to frame the Kowalevski systems within the so-called Gel\\\'fand-Zakharevich bi-Hamiltonian setting for integrable systems.1 aFalqui, Gregorio  uhttp://hdl.handle.net/1963/3244