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Limit theorems in averaging for dynamical systems. (English) Zbl 0841.34048

The ODE system \(dz(t)/dt= \varepsilon B(z(t), f^t y)\) is considered, where \(f^t\) is a so-called suspension flow with the initial condition \(z(0)= x\). The solution of this initial value problem is related to the solution of the averaged system. The main theorem proved in the paper says that under some conditions the difference between the two solutions (divided by \(\varepsilon^{1/2}\)) tends to a Gaussian Markov process that satisfies a certain integral equation as \(\varepsilon\) tends to zero. Several corollaries are also proved.

MSC:

34C29 Averaging method for ordinary differential equations
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
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