Mathematical Surveys and Monographs 1999; 286 pp; hardcover Volume: 66 ISBN10: 0821804979 ISBN13: 9780821804971 List Price: US$89 Member Price: US$71.20 Order Code: SURV/66
 This book studies nonlocal bifurcations that occur on the boundary of the domain of MorseSmale systems in the space of all dynamical systems. These bifurcations provide a series of fascinating new scenarios for the transition from simple dynamical systems to complicated ones. The main effects are the generation of hyperbolic periodic orbits, nontrivial hyperbolic invariant sets and the elements of hyperbolic theory. All results are rigorously proved and explained in a uniform way. The foundations of normal forms and hyperbolic theories are presented from the very first stages. The proofs are preceded by heuristic descriptions of the ideas. The book contains new results, and many results have not previously appeared in monograph form. Readership Graduate students and research mathematicians working in ordinary differential equations; physicists, engineers, computer scientists and mathematical biologists. Reviews "This book is clearly the most complete collection in existence of results for nonlocal bifurcations, excluding homoclinic tangencies. It is clearly written and would serve as a very good introduction to this field. The bibliography is surprisingly extensive, which is important since articles in this field are scattered over very many journals."  Mathematical Reviews Table of Contents  Introduction
 Preliminaries
 Bifurcations in the plane
 Homoclinic orbits of nonhyperbolic singular points
 Homoclinic tori and Klein bottles of nonhyperbolic periodic orbits: Noncritical case
 Homoclinic torus of a nonhyperbolic periodic orbit: Semicritical case
 Bifurcations of homoclinic trajectories of hyperbolic saddles
 Elements of hyperbolic theory
 Normal forms for local families: Hyperbolic case
 Normal forms for unfoldings of saddlenodes
 Bibliography
