Birkhoff normal form via decorated trees
Analysis of PDEs
2025-05-08 v1 Dynamical Systems
Rings and Algebras
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.
Cite
@article{arxiv.2505.04547,
title = {Birkhoff normal form via decorated trees},
author = {Jacob Armstrong-Goodall and Yvain Bruned},
journal= {arXiv preprint arXiv:2505.04547},
year = {2025}
}
Comments
22 pages