NEISHTADT, A., 2017. Averaging method for systems with separatrix crossing. Nonlinearity, 30 (7), pp. 2871–2917.
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 paper was accepted for publication in the journal Nonlinearity and the definitive published version is available at https://doi.org/10.1088/1361-6544/aa712f