从无穷远分支的二阶哈密顿系统的周期解
Periodic solutions of second order Hamiltonian systems bifurcating from infinity
摘要：
本文的目的是研究源于无穷远的自治二阶哈密顿系统的周期解的闭连通集。主要思想是应用第二作者定义的SO（2）-等变梯度算子的度。利用Rabier的结果证明了我们不能用勒雷-绍德尔度来证明本文的主要结果。值得指出的是，由于我们研究连通解集，我们也不能使用Conley指标技术和莫尔斯理论。
英文摘要：
The goal of this article is to study closed connected sets of periodic solutions, of autonomous second order Hamiltonian systems, emanating from infinity. The main idea is to apply the degree for SO(2)-equivariant gradient operators defined by the second author. Using the results due to Rabier we show that we cannot apply the Leray-Schauder degree to prove the main results of this article. It is worth pointing out that since we study connected sets of solutions, we also cannot use the Conley index technique and the Morse theory.
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