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Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications. (English) Zbl 0603.60051
The paper investigates the exponential growth rate (Lyapunov exponent) and rotation number of the harmonic oscillator with random restoring force. The random noise process is assumed to be an ergodic diffusion process. Asymptotic expansions are given when the noise is small, large, rapidly or slowly varying and for the white noise limit.
Reviewer: W.Rümelin

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J99 Markov processes
34F05 Ordinary differential equations and systems with randomness
70L05 Random vibrations in mechanics of particles and systems
93E15 Stochastic stability in control theory
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