Memoirs of the American Mathematical Society 1996; 128 pp; softcover Volume: 121 ISBN10: 0821804413 ISBN13: 9780821804414 List Price: US$43 Individual Members: US$25.80 Institutional Members: US$34.40 Order Code: MEMO/121/578
 In this book, the author investigates a class of smooth one parameter families of vector fields on some \(n\)dimensional manifold, exhibiting a homoclinic bifurcation. That is, he considers generic families \(x_\mu\), where \(x_0\) has a distinguished hyperbolic singularity \(p\) and a homoclinic orbit; an orbit converging to \(p\) both for positive and negative time. It is assumed that this homoclinic orbit is of saddlesaddle type, characterized by the existence of welldefined directions along which it converges to the singularity \(p\). The study is not confined to a small neighborhood of the homoclinic orbit. Instead, the position of the stable and unstable set of the homoclinic orbit is incorporated and it is shown that homoclinic bifurcations can lead to complicated bifurcations and dynamics, including phenomena like intermittency and annihilation of suspended horseshoes. Readership Graduate students and research mathematicians interested in differential equations. Table of Contents  Introduction
 Invariant manifolds and foliations
 Homoclinic intermittency
 Suspended basic sets
 A: Invariant foliations
 Bibliography
