A book on Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics is currently in preparation. The most recent version, with the additions described below, is presently available in draft form. It is expected that newer versions will become available approximately every few months. To download either the Table of Contents, or the Full Book, click on one of the links below. If you are using an older version of Adobe, you may have trouble. However, the newer versions of Adobe should work fine. Patience may be required in downloading the Full Book. Its file is large, approximately 65 MB. 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).
Version of 23 January 2013.
This version has some 2,086 pages (628 pages more than the 24 January 2009 version).
Most chapters, now 34 in number, are essentially complete or at
least contain substantial material. The following additions have been made:
a) The bulk of the material on Duffing's Equation, originally in Chapter 1, has been moved to a
new and
separate Chapter 23. b) Section 2.3.4 on Runge-Kutta integration has been added to describe the use of
Butcher tables and the relation between order and the number of stages in the cases of
both explicit and implicit methods. First Same As Last (FSAL) methods are also
described. Correspondingly, Appendix B has been enlarged to cover the embedded
Runge-Kutta methods Fehlberg 4(5) and Dormand-Prince 5(4). c) The material on geometric integration, originally in Chapter 10, has been moved and
made part of a separate Chapter 11. This new chapter, now devoted to a survey of
integration on manifolds and symplectic integration, is still under construction. d) Appendix S has been added to describe the use of TPSA and its
implementation in Mathematica to compute Taylor maps. e) Chapter 15 on Realistic Transfer Maps for Straight Beam-Line Elements is
complete. Chapters 14 through 19, and their planned sequel, Chapter 20 on
Realistic Transfer Maps for Curved Beam-Line Elements, describe how, for the first time,
it is now possible by using surface methods to compute realistic transfer maps based
on 3-dimensional field data on a mesh as provided by various electromagnetic solvers.
See Figure 15.1.1. In this approach all fringe-field and higher-order multipole
effects are automatically included. Work continues on Chapter 20. f) Apart from some polishing, Section 24.12 of Chapter 24
(General Maps) is now complete. It illustrates the remarkable fact
that a Taylor approximation to the stroboscopic Duffing map, including parameter dependence,
can reproduce the full period doubling Feigenbaum cascade and associated strange
attractor of the exact map. g) Appendix T on Quadrature and Cubature Formulas has been added.