We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct circular orbits in the rotating Kepler problem and observe bifurcations of torus-type orbits. Our setup is motivated by numerical work of Hénon on Hill’s lunar problem.

中文翻译：

---

通过Floer同源性对称周期轨道的分叉

根据局部等变拉格朗日拉比诺维兹弗洛尔同源性，我们给出了可逆哈密顿系统中对称周期轨道分叉的存在的标准。例如，我们考虑旋转开普勒问题中的直接圆形轨道族，并观察圆环型轨道的分叉。Hénon对希尔的月球问题进行的数值研究激发了我们的设置。