A Hierarchy of Multidimensional Hénon-Heiles Systems

A hierarchy of multidimensional Hénon-Heiles (M-H-H) systems are constructed via the x- and t n -higher-order-constrained flows of KdV hierarchy. The Lax representation for the M-H-H hierarchy is determined from the adjoint representation of the auxiliary linear problem for the KdV hierarchy. By using the Lax representation the classical Poisson structure and r-matrix for the hierarchy are found and the Jacobi inversion problem for the hierarchy is constructed.