On the Integrability of Stationary and Restricted Flows of the Kdv Hierarchy

A bi–Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in a case it connects an integrable Hénon–Heiles system and the Garnier system. Moreover a new integrability scheme for Hamiltonian systems is proposed, holding in the standard phase space. Date: Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Piaz.le Europa 1, I34127 Trieste, Italy. 1991 Mathematics Subject Classification. Primary 58F07; Secondary 35Q58. Work partially supported by the GNFM of the Italian CNR and by the project ”Metodi Geometrici e probabilistici in Fisica Matematica” of the Italian MURST.. 1 2 G. TONDO