Abstract
We prove that non resonant isochronous symplectic maps in a neighborhood of an elliptic fixed point are stable for exponentially long times with the inverse of the distance from the fixed point. In the proof we make use of the majorant series method together with an idea for optimizing remainder estimates first applied to Hamiltonian problems by Nekhoroshev.
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Bazzani, A., Marmi, S. & Turchetti, G. Nekhoroshev estimate for isochronous non resonant symplectic maps. Celestial Mech Dyn Astr 47, 333–359 (1989). https://doi.org/10.1007/BF00051010
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DOI: https://doi.org/10.1007/BF00051010