Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Anastassiou, Stavros
Institution: University of Western Macedonia
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213941944