A book on Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics is currently in preparation. The most recent version, described below, is presently available in draft form. It is expected that newer versions will become available approximately every few months. Some figures in the book may not be viewable on the screen because they consist of many very small dots; however, they all should print (with the exception of the stereographic view of the dynamic aperture of the Henon map in Section 1.2, which has yet to be made in digital form). To download either the Table of Contents, or the Full Book, click on one of the links below:
Version of 19 June 2008: This version has some 1,320 pages (118 more than the 3 March 2008 version). Apart from some polishing of figures, Section 1.4.3 on Duffing's Equation is now complete. Appendix J has also been added to illustrate, by way of a simple example, that Feigenbaum period-doubling cascades do not always complete. Substantial portions have been written for Chapter 13 on Realistic Transfer Maps for Straight Beam-Line elements, including related Appendices. Chapter 13 and its planned sequel, Chapter 14 on Realistic Transfer Maps for Curved Beam-Line Elements, describe how, for the first time, it is now possible to compute realistic transfer maps based on 3-dimensional field data on a mesh as provided by various electromagnetic solvers. See Figure 13.1.1. In this approach all fringe-field and higher-order multipole effects are automatically included. Numerous other additions, some larger and some smaller, have also been made, including an extensive discussion of cylindrical harmonics and possible gauges. All known errors have been corrected.