On the integrability of stationary and restricted flows of the KdV hierarchy.

Abstract

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 Henon--Heiles system and the Garnier system. Moreover a new integrability scheme for Hamiltonian systems is proposed, holding in the standard phase space.

25 pages, AMS-LATEX 2.09, no figures, to be published in J. Phys. A: Math. Gen..

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