Symplectic Systems

Abstract

In this chapter we will study the first order matrix difference equation

$$X(t + 1) = M(t)X(t)$$

((3.1))

t ∊ [a, b]. Here b - a is an integer and M(t) is a given 2n x 2n matrix function defined on the discrete interval [a, b] and X(t) is an unknown 2n × m matrix function. In the special case where we have m = 1, we will write (3.1) as the vector equation

$$x(t + 1) = M(t)x(t)$$

((3.2))

.