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}
}
  • F. Adams, A. Bloch
  • Published 4 February 2010
  • Mathematics, Physics
  • Journal of Statistical Physics
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… 

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