A KAM theorem for degenerate infinite-dimensional reversible systems
DOI:
https://doi.org/10.58997/ejde.2024.02Keywords:
KAM theorem; infinite-dimensional reversible system; Russmann non-degeneracy conditionAbstract
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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