Computation of Lie Transformations from a Power Series: Bounds and Optimum Truncation

Details Computation of Lie Transformations from a Power Series: Bounds and Optimum Truncation Computation of Lie Transformations from a Power Series: Bounds and Optimum Truncation

1994-11-03

arxiv.org/abs/chao-dyn/9410011v1

Nonlinear Sciences

Chaotic Dynamics

26 pages, 3 figures (included) file is uuencoded LATEX with macros ps version available from the author

Scientific paper

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.

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