We consider an autonomous Hamiltonian system q¨ + Vq(q) = 0 in R2, where the potential V has a global maximum at the origin and singularities at some points ξ1, ξ 2 ∈ R2{lcub}0{rcub}. Under some compactness conditions on V at infinity and assuming a strong force type condition at the singularities, we study, using variational arguments, the existence of various types of heteroclinic and homoclinic solutions of the system. Imposing some extra geometrical conditions on V, it is shown that the equation admits chaotic solutions.
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机译：我们在 R <中考虑一个自治哈密顿系统q¨ + V q （ q ）= 0 / bold> 2 ，其中潜在的 V 在原点和奇异点ξ 1 ，ξ 2处具有全局最大值∈ R 2 {lcub} 0 {rcub}。在无穷大的 V 上的某些紧致性条件下，并假设奇异性为强力类型条件，我们使用变分参数研究系统的各种类型的异斜度和同斜度解的存在。在 V 上施加一些额外的几何条件，表明该方程允许混沌解。
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