This paper studies the dynamics of a family of Hamiltonian systems that originate from Friedman–Lematre–Robertson–Walker space-times with a coupled field and non-zero curvature. In four distinct cases, previously considered by Maciejewski, Przybylska, Stachowiak and Szydowski, it is shown that there are homoclinic connections to invariant submanifolds and the connections split. These results imply the non-existence of a real-analytic integral independent of the Hamiltonian.

中文翻译：

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具有耦合场和非零曲率的宇宙学模型中的马蹄形和不变环面部分由加拿大自然科学和工程研究委员会资助 320 852。

本文研究了源自 Friedman-Lematre-Robertson-Walker 时空的具有耦合场和非零曲率的哈密顿系统家族的动力学。在 Maciejewski、Przybylska、Stachowiak 和 Szydowski 之前考虑的四种不同情况下，表明存在与不变子流形的同宿连接并且连接分裂。这些结果意味着不存在独立于哈密顿量的实解析积分。