Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Riahi, Hasna

Softcover

ISBN 10: 0821808737 ISBN 13: 9780821808733

Publisher: American Mathematical Society, 1999

Synopsis

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 Palais-Smale 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 4-body type problems then generalized to n-body type problems.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1999
• Language: English
• ISBN 10: 0821808737
• ISBN 13: 9780821808733
• Binding: Paperback
• Number of pages: 658