| Abstract: |
| We will talk about the Maslov-type index $i_{L_{0}}$ on the brake orbit boundary for symplectic paths starting from identity $I_{2n}$ for any positive integer $n$. we prove that $-n\le i_{L_{0}}(\ga^m)-m\hat{i}_{L_{0}}(\ga)\le 0$ for any positive integer $m$ and any symplectic path $\ga$ starting from identity, where $\hat{i}_{L_{0}}$ is the mean index of $i_{L_{0}}$, $\ga^m$ is the $m$-th iteration of $\ga$ in the sense of brake orbit boundary. As application, we study the multiplicity of brake orbits of Hamiltoninan equation on tori. This is a joint work with Hui Liu and Fanjing Wang. |
|