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arXiv:2505.04547 [math.AP]AbstractReferencesReviewsResources

Birkhoff normal form via decorated trees

Jacob Armstrong-Goodall, Yvain Bruned

Published 2025-05-07Version 1

We derive an explicit tree based ansatz for the Birkhoff normal form up to any order in the context of Hamiltonian PDEs. To do so we make use of a tree based representation of iterated Poisson brackets to encode the nested Taylor expansions along flows of a sequence of symplectic transformations. As an example we consider the cubic Schr\"odinger equation.

Comments: 22 pages
Categories: math.AP, math.DS, math.RA
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