KAM theory for the reversible perturbations of 2D linear beam equations

Ge, Chuanfang; Geng, Jiao; Lou, Zhaowei

doi:10.1007/s00209-020-02575-9

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2021

2024

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Cited by 7 publications

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“…On the other hand, KAM theory for infinite-dimensional Hamiltonian systems has also been extended to infinite-dimensional reversible systems [2,4,7,9,12,11,13,14,24]. However, to the best of our knowledge, these results are all based on classical non-degeneracy conditions, and there is still no works on KAM theory for degenerate infinite-dimensional reversible systems.…”

Section: Introductionmentioning

confidence: 99%

KAM theorem for degenerate infinite-dimensional reversible systems

Lou,

2024

ejde

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In this article, we establish a Kolmogorov-Arnold-Moser (KAM) theorem for degenerate infinite-dimensional reversible systems under a non-degenerate condition of Russmann type. This theorem broadens the scope of applicability of degenerate KAM theory, previously confined to Hamiltonian systems, by incorporating infinite-dimensional reversible systems. Using this theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of non-Hamiltonian but reversible beam equations with non-linearities in derivatives. For more information see https://ejde.math.txstate.edu/Volumes/2024/02/abstr.html

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