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arXiv · 2505.04547

Birkhoff normal form via decorated trees

Jacob Armstrong-Goodall·Yvain Bruned
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Abstract

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.

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Jacob Armstrong-Goodall, Yvain Bruned. 2025-05-07. Birkhoff normal form via decorated trees. https://arxiv.org/abs/2505.04547

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