%0 Journal Article %J J. Phys. A 34 (2001) 2077-2085 %D 2001 %T Lax representation and Poisson geometry of the Kowalevski top %A Gregorio Falqui %X 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. %B J. Phys. A 34 (2001) 2077-2085 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/3244 %1 1457 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-05T09:26:47Z\\nNo. of bitstreams: 1\\nLaxrepresentation.pdf: 214031 bytes, checksum: e7ebdee1c74f45ce326005194acedae9 (MD5) %R 10.1088/0305-4470/34/11/301