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A Note on the KAM Theorem for Symplectic Mappings

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Abstract

The mapping version of Pöschel's theory on differentiable foliation structures of invariant tori is presented and the relevant estimates explicitly in terms of the diophantine constant and the nondegeneracy parameters of frequency maps are given. As a direct application of the main result, a generalization of Moser's small twist theorem to high dimensions is given.

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  1. Institute of Mathematics, Academia Sinica, Beijing, 100080, China

    Zai-jiu Shang

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  1. Zai-jiu Shang
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Shang, Zj. A Note on the KAM Theorem for Symplectic Mappings. Journal of Dynamics and Differential Equations 12, 357–383 (2000). https://doi.org/10.1023/A:1009068425415

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