Memoirs of the American Mathematical Society 2014; 115 pp; softcover Volume: 227 ISBN10: 0821890182 ISBN13: 9780821890189 List Price: US$76 Individual Members: US$45.60 Institutional Members: US$60.80 Order Code: MEMO/227/1067
 In this monograph the authors introduce a new method to study bifurcations of KAM tori with fixed Diophantine frequency in parameterdependent Hamiltonian systems. It is based on Singularity Theory of critical points of a realvalued function which the authors call the potential. The potential is constructed in such a way that: nondegenerate critical points of the potential correspond to twist invariant tori (i.e. with nondegenerate torsion) and degenerate critical points of the potential correspond to nontwist invariant tori. Hence, bifurcating points correspond to nontwist tori. Table of Contents Part 1: Introduction and preliminaries  Introduction
 Preliminaries
Part 2: Geometrical properties of KAM invariant tori  Geometric properties of an invariant torus
 Geometric properties of fibered Lagrangian deformations
Part 3: KAM results  Nondegeneracy on a KAM procedure with fixed frequency
 A KAM theorem for symplectic deformations
 A Transformed Tori Theorem
Part 4: Singularity theory for KAM tori  Bifurcation theory for KAM tori
 The closetointegrable case
Appendices  Appendix A. Hamiltonian vector fields
 Appendix B. Elements of singularity theory
 Bibliography
