Lie Methods in Optics pp 45-103 | Cite as

# Lie series, Lie transformations, and their applications

## Abstract

This paper is an exposition of the basic properties of Lie series and Lie transformations, which are now finding widespread applications. The applications are of two types: expanding solutions of Hamilton's equations and reducing (simplifying) Hamiltonians to normal form. The expansions are not power series but rather *factored product expansions*. These expansions have the advantage that the approximating systems are also hamiltonian. The normal form procedure has the advantage that it is canonical and explicit. In both cases the methods used are chosen so that they are easy to implement in a general purpose computer symbol manipulator.

## Keywords

Hamiltonian System Poisson Bracket Canonical Transformation Power Series Expansion Perturbation Equation## Preview

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## References

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