Geodesic
Krylov--Bogolyubov averaging
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 3, pp. 427-444

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A modified approach to the classical Krylov–Bogolyubov averaging method is presented. It was developed recently for studying partial differential equations, enables one to treat Lipschitz perturbations of linear systems with purely imaginary spectrum, and may be generalized to the case of systems of PDEs with small non-linearities. Bibliography: 10 titles.
Keywords: Krylov–Bogolyubov method, locally Lipschitz vector-field, Hamiltonian equations. 
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     title = {Krylov--Bogolyubov averaging},
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W. Jian; S. B. Kuksin; Y. Wu. Krylov--Bogolyubov averaging. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 75 (2020) no. 3, pp. 427-444. http://geodesic.mathdoc.fr/item/RM_2020_75_3_a1/