量子谐振子的KAM
KAM for the quantum harmonic oscillator
摘要：
本文证明了无穷维Hamilton系统的一个抽象KAM定理。这一结果推广了S.B. Kuksin和J. Pöschel，并使用H. Eliasson和S.B. Kuksin。作为应用，我们证明了某些一维非线性薛定谔方程存在多个拟周期解。在第二个应用中，我们证明了一维薛定谔方程在调和势和拟周期势下的约化。
英文摘要：
In this paper we prove an abstract KAM theorem for infinite dimensional Hamiltonians systems. This result extends previous works of S.B. Kuksin and J. Pöschel and uses recent techniques of H. Eliasson and S.B. Kuksin. As an application we show that some 1D nonlinear Schrödinger equations with harmonic potential admits many quasi-periodic solutions. In a second application we prove the reducibility of the 1D Schrödinger equations with the harmonic potential and a quasi periodic in time potential.
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