Abstract
We consider a hierarchy of many-particle systems on the line with polynomial potentials separable in parabolic coordinates.The first non-trivial member of this hierarchy is a generalization of an integrable case of the Hénon-Heiles system.We give a Lax representation in terms of 2 × 2 matrices for the whole hierarchy and construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables.A Yang-Baxter equation of dynamical type is proposed.Classical integration in a particular case is carried out and quantization of the system is discussed with the help of separation variables.