Let v be a nonsingular Morse–Smale vector field in the kernel of a contact form α, with Reeb vector field \(\xi\), defined on M³. We establish that the associated variational problem at infinity defined by the action functional on the stratified space \(\bigcup \Gamma_{2k}\) of curves made of \(\xi\)-pieces of orbits alternating with \(\pm v\)-pieces of orbits satisfies the Palais–Smale condition. This result takes a more special form for the standard contact structure of S³.

中文翻译：

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接触形式几何的无穷大变化

令v为接触形式α的核中的非奇异Morse-Smale向量场，其中Reeb向量场\（\ xi \）在M ³上定义。我们建立了由\（\ xi \）组成的曲线的分层空间\（\ bigcup \ Gamma_ {2k} \）上的作用函数所定义的无穷大相关变分问题，这些曲线与\（\ pm v \） -轨道的各个部分满足Palais–Smale的条件。对于S ³的标准触点结构，此结果采用更特殊的形式。