PreprintCC BY 4.0arXiv
Combinatorics of Hamiltonian Normal Forms
Abstract
We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point by an explicit formula in terms of the original Hamiltonian, avoiding the normalization procedure. In the case of one degree of freedom we compute the normal form as an explicit nonlinear functional, applied to the original Hamiltonian. In arbitrary dimension the corresponding formulas are more complicated but still explicit.
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BibTeX
@misc{treschev2026combinatorics,
title = {{Combinatorics of Hamiltonian Normal Forms}},
author = {Dmitry Treschev},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.02839},
eprint = {2605.02839},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.02839},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Combinatorics of Hamiltonian Normal Forms
AU - Dmitry Treschev
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2605.02839
UR - https://arxiv.org/abs/2605.02839
AB - We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point by an explicit formula in terms of the original Hamiltonian, avoiding the normalization procedure. In the case of one degree of freedom we compute the normal form as an explicit nonlinear functional, applied to the original Hamiltonian. In arbitrary dimension the corresponding formulas are more complicated but still explicit.
ER -