Averaging methods in nonlinear dynamical systems / J. A. Sanders, F. Verhulst, J. Murdock

This book is not only a revision of the first edition published 22 years ago, its extended content reflects also special developments in the theory of dynamical systems in the mentioned period: normal forms, invariant manifolds, perturbation theory.

The new material is organized in four chapters and two appendices. Chapter 6 is devoted to periodic averaging and hyperbolicity (interaction of the Morse-Smale theory including shadowing with averaging), Chapter 11 is entitled “classical (first level) normal form theory” and gives an introduction into the abstract formulation of the NFT, Chapter 12 treats nilpotent (classical) normal forms including computational aspects. Chapter 13 is concerned with higher-level NFT (continuation of the abstract treatment).

The new appendix C “invariant manifolds by averaging” considers the deformation of normally hyperbolic manifolds and different scenarios for the emergence of tori in some examples. Appendix E is devoted to averaging methods for partial differential equations. Since the results in that field are still fragmented, this section provides a survey on literature for weakly nonlinear PDE’s. (Zentralblatt)