KAM theorem for degenerate infinite-dimensional reversible systems

Abstract

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