  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 H\'enon-Heiles
system. We give a Lax representation in terms of $2\times 2$ 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. This paper was published in the rary issues: Sfb 288
Preprint No. 110, Berlin and Nonlinear Mathematical Physics, {\bf 1(3)},
275-294 (1994)
