Computation of Lie Transformations from a Power Series: Bounds and   Optimum Truncation
  The problem considered is the computation of an infinite product (composition) of Lie transformations generated by homogeneous polynomials of increasing order from a given convergent power series. Bounds are computed for the infinitesimal form of Lie transformations. The results obtained do not guarantee convergence of the product. Instead, the optimum truncation is determined by minimizing the terms of order n+1 that remain after the first n Lie transformations have been applied. 
Ivan Gjaja (Center for Nonlinear Studies, Los Alamos National   Laboratory, Los Alamos, NM 87545)