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arXiv · 2609.21417

Normal forms and first integrals of planar maps at elliptic fixed points

Stavros Anastassiou
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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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Stavros Anastassiou. 2026-09-18. Normal forms and first integrals of planar maps at elliptic fixed points. https://arxiv.org/abs/2609.21417

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