Study of the critical points at infinity arising from the failure of the Palais-Smale condition for n-body type problems
著者
書誌事項
Study of the critical points at infinity arising from the failure of the Palais-Smale condition for n-body type problems
（Memoirs of the American Mathematical Society, no. 658）
American Mathematical Society, 1999
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注記
"March 1999, volume 138, number 658 (first of 4 numbers)" -- T.p.
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
Introduction Breakdown of the Palais-Smale condition Morse Lemma near infinity A modified functional for the 4-body problem Retraction theorem and related results for the 4-body problem Generalization of the n-body problem.
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