# Hill’s Equation with Random Forcing Parameters: Determination of Growth Rates Through Random Matrices

@article{Adams2010HillsEW, title={Hill’s Equation with Random Forcing Parameters: Determination of Growth Rates Through Random Matrices}, author={Fred C. Adams and Anthony M. Bloch}, journal={Journal of Statistical Physics}, year={2010}, volume={139}, pages={139-158} }

This paper derives expressions for the growth rates for the random 2×2 matrices that result from solutions to the random Hill’s equation. The parameters that appear in Hill’s equation include the forcing strength qk and oscillation frequency λk. 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 (qk,λk) lead to matrix elements that vary from…

## 5 Citations

Random Hill’s Equations, Random Walks, and Products of Random Matrices

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Hill’s equations arise in a wide variety of physical problems, and are specified by a natural frequency, a periodic forcing function, and a forcing strength parameter. This classic problem can be…

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Hill's equations arise in a wide variety of physical problems, and are specified by a natural frequency, a periodic forcing function, and a forcing strength parameter. This classic problem is…

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A perturbation method for determining the moment stability of linear ordinary differential equations with parametric forcing bycolored noise based on a ladder operator approach to the vector Ornstein-Uhlenbeck process.

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We prove a central limit theorem (CLT) for the product of a class of random singular matrices related to a random Hill’s equation studied by Adams–Bloch–Lagarias. The CLT features an explicit formula…

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