标题： 弱湍流的玩具模型中的离散束缚态及其对不变测度的影响 显示英文标题

标题： Discrete Bound States in a Toy Model for Weak Turbulence and Implications for the Invariant Measure

摘要： 一个模型哈密顿动力系统已被推导出来，用于研究环面上三次非聚焦非线性薛定谔方程中的频率级联。 在此，我们探讨通过分类固定质量下的能量极小值来探索动力学的规范系综形式，并表征这些极小值附近不变测度的框架。 显示英文摘要

摘要： A model Hamiltonian dynamical system has been derived to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus. Here, we explore the framework for exploring a canonical ensemble formulation of the dynamics through classification of energy minimizers for fixed mass and characterizing the invariant measure in a neighborhood of those minimizers.