Academy of Mathematics and Systems Science, CAS Colloquia & Seminars Speaker: Prof. Hu Xijun, Department of Mathematics, Shandong University Title: Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to N-body problem Time: 2010.1.22 4:00pm Venue: Room:S703 Abstract: Using the Maslov index theory in symplectic geometry, we build up some stability criteria for symmetric periodic orbits in a Hamiltonian system, which is motivated by the recent discoveries in the n-body problem. The key ingredient is a generalized Bott-type iteration formula for periodic solution in the presence of finite group action on the orbit. As an application we consider the stability problem of the celebrated figure-eight orbit due to Chenciner and Montgomery in the planar three-body problem with equal masses, and we clarify the relationship between linear stability and its variational nature on various loop spaces. The application to the elliptic Lagrangian solutions is also given. This is a joint work with Shanzhong Sun. Affiliation: