A Maslov-type index theory for symplectic paths
A Maslov-type index theory for symplectic paths
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DOI：
10.12775/tmna.1997.021
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发表时间：
1997-09
影响因子：
0.7
通讯作者：
Y. Long
中科院分区：
文献类型：
--
作者：
Y. Long
本文将文献[7]、[15]、[10]和[18]中定义的Maslov型指标理论推广到所有连续退化辛路，给出了该指标理论对所有连续辛路的拓扑刻画，并研究了它的基本性质。假设τ > 0。考虑一个τ -周期对称连续的2n × 2n矩阵函数B（t），即B ∈ C（Sτ，Ls（R）），Sτ = R/（τZ），L（R2 n）是所有真实的2n×2n矩阵的集合，Ls（R）是所有对称矩阵的子集.一阶线性哈密顿系统的基本解γ
In this paper, we extend the Maslov-type index theory defined in [7], [15], [10], and [18] to all continuous degenerate symplectic paths, give a topological characterization of this index theory for all continuous symplectic paths, and study its basic properties. Suppose τ > 0. We consider an τ -periodic symmetric continuous 2n × 2n matrix function B(t), i.e. B ∈ C(Sτ ,Ls(R)) with Sτ = R/(τZ), L(R2n) being the set of all real 2n×2n matrices, and Ls(R) being the subset of all symmetric matrices. It is well-known that the fundamental solution γ of the linear first order Hamiltonian system