KAM theorem for a Hamiltonian system with sublinear growth frequencies at infinity. (English) Zbl 1454.37070
Summary: 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.
MSC:
| 37K55 | Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems |
| 35B10 | Periodic solutions to PDEs |
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