Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator and Applications
- 1 June 1986
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 46 (3) , 427-450
- https://doi.org/10.1137/0146030
Abstract
We construct asymptotic expansions for the exponential growth rate (Lyapunov exponent) and rotation number of the random oscillator when the noise is large, small, rapidly varying or slowly varying. We then apply our results to problems in the stability of the random oscillator, the spectrum of the one-dimensional random Schrödinger operator and wave propagation in a one-dimensional random medium.Keywords
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