TY - JOUR T1 - Lax representation and Poisson geometry of the Kowalevski top JF - J. Phys. A 34 (2001) 2077-2085 Y1 - 2001 A1 - Gregorio Falqui AB - We 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. PB - IOP Publishing UR - http://hdl.handle.net/1963/3244 U1 - 1457 U2 - Mathematics U3 - Mathematical Physics ER -