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Normal forms and first integrals of planar maps at elliptic fixed points
Abstract
We study real-analytic, planar, maps, at a neighbourhood of an elliptic fixed point. We construct normal forms for them, when they admit a real-analytic first integral. We prove that a second first integral, when it exists, forces their linearisation. We consider both the resonant and the non-resonant case, whether the maps preserve a symplectic form or not. The second first integral is allowed to be smooth, real-meromorphic or real-analytic.
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BibTeX
@misc{anastassiou2026normal,
title = {{Normal forms and first integrals of planar maps at elliptic fixed points}},
author = {Stavros Anastassiou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21417},
eprint = {2609.21417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21417},
}
RIS
TY - UNPB
TI - Normal forms and first integrals of planar maps at elliptic fixed points
AU - Stavros Anastassiou
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21417
UR - https://arxiv.org/abs/2609.21417
AB - We study real-analytic, planar, maps, at a neighbourhood of an elliptic fixed point. We construct normal forms for them, when they admit a real-analytic first integral. We prove that a second first integral, when it exists, forces their linearisation. We consider both the resonant and the non-resonant case, whether the maps preserve a symplectic form or not. The second first integral is allowed to be smooth, real-meromorphic or real-analytic.
ER -