Nonlinear Dynamics: Exploration Through Normal Forms

Assembling a variety of ideas they have developed in investigating a small portion non nonlinear dynamics, Kahn and Zarmi concentrate on constructing an exposition of the method of normal forms and its application to ordinary differential equations through perturbation analysis. In particular, they use the inherent freedom in the expansion to obtain expressions that are compact and have computational advantages, which they illustrate in a number of applications. Among their topics are basic concepts, naive perturbation theory, problems with eigenvalues that have a negative real part, non-autonomous oscillatory systems, and problems with a zero eigenvalue. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Exposition for advanced undergraduates and graduate students covers the method of normal forms and its application to ordinary differential equations through perturbation analysis. Numerous examples of equations encountered in areas of science and engineering. 1998 edition.
Geared toward advanced undergraduates and graduate students, this exposition covers the method of normal forms and its application to ordinary differential equations through perturbation analysis. In addition to its emphasis on the freedom inherent in the normal form expansion, the text features numerous examples of equations, the kind of which are encountered in many areas of science and engineering. The treatment begins with an introduction to the basic concepts underlying the normal forms. Coverage then shifts to an investigation of systems with one degree of freedom that model oscillations, in which the force has a dominant linear term and a small nonlinear one. The text considers a variety of nonautonomous systems that arise during the study of forced oscillatory motion. Topics include boundary value problems, connections to the method of the center manifold, linear and nonlinear Mathieu equations, pendula, Nuclear Magnetic Resonance, coupled oscillator systems, and other subjects. 1998 edition.