论文标题
离散哈密顿系统的莫尔斯指数和马斯洛夫型索引
Morse index and Maslov-type index of the discrete Hamiltonian system
论文作者
论文摘要
在本文中，我们给出了离散哈密顿系统的Maslov型索引的定义，并获得了离散的哈密顿系统的Morse索引和Maslov-Type索引的关系，这是案例$ω= 1 $ in \ in \ cite {ros1}}的概括{ros1}，\ cite {ros2}，\ cite {ros2} and casite {ros2} anf cesite {ros2 and c。 u} $通过直接方法与\ cite {ros1}，\ cite {ros2}和\ cite {maz1}不同的方法不同。此外，已证明了离散哈密顿系统的分裂数字$s_Ω$，因此在\ cite {bot1}中的索引迭代理论和\ cite {lon4}也适用于离散的汉密尔顿系统案例。
In this paper, we give the definition of Maslov-type index of the discrete Hamiltonian system, and obtain the relation of Morse index and Maslov-type index of the discrete Hamiltonian system which is a generalization of case $ω=1$ in \cite{RoS1}, \cite{RoS2} and \cite{Maz1} to case $ω\in {\bf U}$ via direct method which is different from that of \cite{RoS1}, \cite{RoS2} and \cite{Maz1}. Moreover well-posedness of the splitting numbers $S_ω$ of the discrete Hamiltonian system is proven, thus index iteration theories in \cite{Bot1} and \cite{Lon4} are also valid for the discrete Hamiltonian system case.
