# Krylov--Bogolyubov averaging

## TL;DR

This paper introduces a modified Krylov-Bogolyubov averaging method tailored for PDEs, enabling the analysis of Lipschitz perturbations of linear systems with imaginary spectra and extending to PDEs with small nonlinearities.

## Contribution

It develops a new averaging approach specifically designed for PDEs, improving the analysis of systems with small nonlinearities and Lipschitz perturbations.

## Key findings

- Effective treatment of Lipschitz perturbations in linear systems
- Extension of averaging methods to PDEs with small nonlinearities
- Potential for broader application in nonlinear PDE analysis

## Abstract

We present the modified approach to the classical Bogolyubov-Krylov averaging, developed recently for the purpose of PDEs. It allows to treat Lipschitz perturbations of linear systems with pure imaginary spectrum and may be generalized to treat PDEs with small nonlinearities.