Memoirs of the American Mathematical Society 1999; 112 pp; softcover Volume: 138 ISBN10: 0821808737 ISBN13: 9780821808733 List Price: US$47 Individual Members: US$28.20 Institutional Members: US$37.60 Order Code: MEMO/138/658
 In this work, the author examines the following: When the Hamiltonian system \(m_i \ddot{q}_i + (\partial V/\partial q_i) (t,q) =0\) with periodicity condition \(q(t+T) = q(t),\; \forall t \in \mathfrak R\) (where \(q_{i} \in \mathfrak R^{\ell}\), \(\ell \ge 3\), \(1 \le i \le n\), \(q = (q_{1},...,q_{n})\) and \(V = \sum V_{ij}(t,q_{i}q_{j})\) with \(V_{ij}(t,\xi)\) \(T\)periodic in \(t\) and singular in \(\xi\) at \(\xi = 0\)) is posed as a variational problem, the corresponding functional does not satisfy the PalaisSmale condition and this leads to the notion of critical points at infinity. This volume is a study of these critical points at infinity and of the topology of their stable and unstable manifolds. The potential considered here satisfies the strong force hypothesis which eliminates collision orbits. The details are given for 4body type problems then generalized to nbody type problems. Readership Graduate students and research mathematicians working in applications of Morse theory and the study of dynamical systems. Table of Contents  Introduction
 Breakdown of the PalaisSmale condition
 Morse Lemma near infinity
 A modified functional for the 4body problem
 Retraction theorem and related results for the 4body problem
 Generalization of the nbody problem
