Hill's Equation with Random Forcing Parameters: Determination of Growth
  Rates through Random Matrices
  This paper derives expressions for the growth rates for the random 2 x 2
matrices that result from solutions to the random Hill's equation. The
parameters that appear in Hill's equation include the forcing strength and
oscillation frequency. The development of the solutions to this periodic
differential equation can be described by a discrete map, where the matrix
elements are given by the principal solutions for each cycle. Variations in the
forcing strength and oscillation frequency lead to matrix elements that vary
from cycle to cycle. This paper presents an analysis of the growth rates
including cases where all of the cycles are highly unstable, where some cycles
are near the stability border, and where the map would be stable in the absence
of fluctuations. For all of these regimes, we provide expressions for the
growth rates of the matrices that describe the solutions.
