Hill's Equation with Random Forcing Terms

Motivated by a class of orbit problems in astrophysics, this paper considers solutions to Hill's equation with forcing strength parameters that vary from cycle to cycle. The results are generalized to include period variations from cycle to cycle. The development of the solutions to the differential equation is governed by a discrete map. For the general case of Hill's equation in the unstable limit, we consider separately the case of purely positive matrix elements and those with mixed signs; we then find exact expressions, bounds, and estimates for the growth rates. We also find exact expressions, estimates, and bounds for the infinite products of several 2

• Type: Journal
• Year: 2008
• Where: SIAMAM
• Authors: Fred C. Adams, Anthony M. Bloch
• Keywords: Discrete Map, Exact Expressions, Matrix Elements, SIAMAM 2008