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Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems

Hasna Riahi

出版	American Mathematical Soc., 1999
主題	Mathematics / GeneralMathematics / Mathematical AnalysisMathematics / Topology
ISBN	08218087379780821808733
URL	http://books.google.com.hk/books?id=zJfTCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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.