论文标题
在哈密顿系统中非周期轨道的平均指数
Mean index for non-periodic orbits in Hamiltonian systems
论文作者
论文摘要
在本文中，我们定义了哈密顿系统中非周期轨道的平均指数并研究其性质。通常，平均指数是R的间隔，该间隔在系统上均匀连续。我们表明，索引间隔是准周期轨道的点。平均指数可以视为约翰逊和摩泽尔在几乎周期性的施罗宾格运营商研究中定义的旋转数的概括。在他们的作品中，我们研究了线性操作员的弗雷德霍尔姆属性和本文结尾处的平均指数的关系。
In this paper, we define mean index for non-periodic orbits in Hamiltonian systems and study its properties. In general, the mean index is an interval in R which is uniformly continuous on the systems. We show that the index interval is a point for a quasi-periodic orbit. The mean index can be considered as a generalization of rotation number which defined by Johnson and Moser in the study of almost periodic Schrodinger operators. Motivated by their works, we study the relation of Fredholm property of the linear operator and the mean index at the end of the paper.
