Averaging method for systems with separatrix crossing

Abstract

The averaging method provides a powerful tool for studying evolution in near-integrable systems. Existence of separatrices in the phase space of the underlying integrable system is an obstacle for application of standard results that justify using of averaging. We establish estimates that allow to use averaging method when the underlying integrable system is a system with one rotating phase, and the evolution leads to separatrix crossings.

This is an author-created, un-copyedited version of the article accepted for publication in Nonlinearity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

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