Linear Hamiltonian Systems

Abstract

In this chapter we study Hamiltonian systems which are linear differential equations. Many of the basic facts about Hamiltonian systems and symplectic geometry are easy to understand in this simple context. The basic linear algebra introduced in this chapter is the cornerstone of many of the later results on nonlinear systems. Some of the more advanced results which require a knowledge of multilinear algebra or the theory of analytic functions of a matrix are relegated to the appendices or references to the literature. These results are not important for the main development.