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arXiv · 1810.03135

On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range

Yuan Wu·Xiaoping Yuan
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Abstract

In this paper, it is proved that the infinite KAM torus with prescribed frequency exists in a sufficiently small neighborhood of a given $ I^{0}$ for nearly integrable and analytic Hamiltonian system $ H(I,\theta) = H_{0}(I)+ \epsilon H_{1}(I,\theta)$ of infinite degree of freedom and of short range. That is to say, we will give an extension of the original Kolmogorov theorem to the infinite-dimensional case of short range. The proof is based on the approximation of finite-dimensional Kolmogorov theorem and an improved KAM machinery which works for the normal form depending on initial $ I^{0}$.

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Yuan Wu, Xiaoping Yuan. 2018-10-07. On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range. https://arxiv.org/abs/1810.03135

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