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Lie Methods in Optics pp 45–103Cite as

Lie series, Lie transformations, and their applications

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Part of the book series: Lecture Notes in Physics ((LNP,volume 250))

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.

Partially supported by NSF grant # MCS-8102983 and the U.S. Army Research Office.

This chapter was written by the author using a T-ROFF text processor, and a diskette was sent to the editors, who used the EMACS editor to turn it into a TEX file, half by replace string commands, half by hand. Editorial work consisted of proofreading, formatting, and deepening the segmentation. (Editor's note.)

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Authors
  1. Stanly Steinberg
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J. Sánchez Mondragón K. B. Wolf

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© 1986 Springer-Verlag

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Steinberg, S. (1986). Lie series, Lie transformations, and their applications. In: Sánchez Mondragón, J., Wolf, K.B. (eds) Lie Methods in Optics. Lecture Notes in Physics, vol 250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16471-5_3

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