A description of Lax type integrable dynamical systems via the Marsden-Weinstein reduction method

► We develop the Marsden-Weinstein reduction method for constructing Lax type integrable dynamical systems. ► Based on the Lie-algebraic approach a new so called D-structure is devised. ► There is described a relationship between the D-structure versus the classical R-structure. ► The reduced Poisson structure is calculated, an infinite hierarchy of commuting invariants is constructed.