论文标题
光谱流，布鲁维尔学位和希尔的决定因素公式
Spectral flow, Brouwer degree and Hill's determinant formula
论文作者
论文摘要
2005年，Musso，Pejsachowicz引入了根据决定符地图的Brouwer程度定义的新拓扑不变性，并且是沿着半摩西式大地测量的结合点的名字作者。这种不变的定义是根据线性二阶二阶dirichlet边界价值问题的综合家族的悬架定义的。 在本文中，从这个结果开始，我们将这种不变性概括为一般的自我偶像摩尔斯 - 莫尔斯 - 斯图尔姆系统，我们证明了一个新的光谱流程公式。最后，我们讨论了这种光谱流程公式与山丘的决定因素公式之间的关系，并将这种不变性应用于检测哈密顿系统的周期性轨道的不稳定性。
In 2005 a new topological invariant defined in terms of the Brouwer degree of a determinant map, was introduced by Musso, Pejsachowicz and the first name author for counting the conjugate points along a semi-Riemannian geodesic. This invariant was defined in terms of a suspension of a complexified family of linear second order Dirichlet boundary value problems. In this paper, starting from this result, we generalize this invariant to a general self-adjoint Morse-Sturm system and we prove a new spectral flow formula. Finally we discuss the relation between this spectral flow formula and the Hill's determinant formula and we apply this invariant for detecting instability of periodic orbits of a Hamiltonian system.
