A connection between the Henon–Heiles system and the Garnier system

A remarkable map between a generalized Henon–Heiles system and the Garnier system is obtained by means of a detailed comparison between two finite–dimensional reduction methods for soliton equations: the stationary flows and the restricted flows. The role of the Gelfand–Dickey polynomials and of the KdV Poisson pencil in this construction is emphasized.