Hill's Equation with Random Forcing Parameters: The Limit of Delta Function Barriers

Understand

This paper considers random Hill's equations in the limit where the periodic forcing function becomes a Dirac delta function.

• For this class of equations, the forcing strength $q_k$, the oscillation frequency $\af_k$, and the period are allowed to vary from cycle to cycle.
• Such equations arise in astrophysical orbital problems in extended mass distributions, in the reheating problem for inflationary cosmologies, and in periodic Schr{\"o}dinger equations.
• The growth rates for solutions to the periodic differential equation can be described by a matrix transformation, where the matrix elements vary from cycle to cycle.