KAM Theorem for a Hamiltonian System with Sublinear Growth Frequencies at Infinity

  • Xindong XuEmail author
Original Article


We prove an infinite-dimensional KAM theorem for a Hamiltonian system with sublinear growth frequencies at infinity. The main purpose is to present a new and simple method to study the dynamics of such Hamiltonian. We will outline the main difficulty due to sublinear growth frequencies and then present the method to overcome this problem. We apply this theorem to a fractional nonlinear Schrödinger equation on the torus \({\mathbb {T}}\), thus proving existence and stability of quasi–periodic solutions.


KAM theorem Sublinear growth frequencies Fractional Schrödinger equation 

Mathematics Subject Classification

Primary 37K55 35B10 



The author was supported by the NSFC, Grant No. 11771077, 11571072. The author is thankful to Professor M. Gao for her valuable suggestion.


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Authors and Affiliations

  1. 1.School of MathematicsSoutheast UniversityNanjingPeople’s Republic of China

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