Memoirs of the American Mathematical Society 1996; 100 pp; softcover Volume: 121 ISBN10: 082180443X ISBN13: 9780821804438 List Price: US$44 Individual Members: US$26.40 Institutional Members: US$35.20 Order Code: MEMO/121/577
 In this book, the "canard phenomenon" occurring in Van der Pol's equation \(\epsilon \ddot x+(x^2+x)\dot x+xa=0\) is studied. For sufficiently small \(\epsilon >0\) and for decreasing \(a\), the limit cycle created in a Hopf bifurcation at \(a = 0\) stays of "small size" for a while before it very rapidly changes to "big size", representing the typical relaxation oscillation. The authors give a geometric explanation and proof of this phenomenon using foliations by center manifolds and blowup of unfoldings as essential techniques. The method is general enough to be useful in the study of other singular perturbation problems. Readership Graduate students, mathematicians, physicists, and engineers interested in ordinary differential equations, specifically singular perturbation problems. Table of Contents  Statement of the result: the "canard phenomenon" for the singular Van der Pol equation
 Global desingularization
 Foliations by center manifolds
 The canard phenomenon
 References
 Appendix: on the proof of theorem 18 (by Chengzhi Li)
