Averaging with a time-dependent perturbation parameter

Abstract

Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time behavior for solutions of a general class of systems. We thus propose our result to be applicable to a wide range of problems in spatially homogenous cosmology with oscillatory behavior. Mathematically the theorem builds upon the standard theory of averaging in non-linear dynamical systems.

arXiv commentchanges from the previous version: extended introduction; additional references

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• Averaging Generalized Scalar Field Cosmologies II: Locally Rotationally Symmetric Bianchi I and flat Friedmann-Lemaître-Robertson-Walker models
• Scalar field evolution at background and perturbation levels for a broad class of potentials
• Averaging method and coherence applied to Rabi oscillations in a two-level system