Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing on the resonant approximation that accurately captures in a simplified form the long-term evolution of small initial data. Topics covered include turbulent and regular motion, dynamical recurrences analogous to the Fermi–Pasta–Ulam phenomena in oscillator chains, and relations between AdS dynamics and nonrelativistic nonlinear Schrdinger equations in harmonic potentials. Special mention is given to the way the classical dynamics of weakly nonlinear strongly resonant systems is illuminated by perturbative considerations within the corresponding quantum theories, in particular, in relation to quantum chaos theory.

回顾了反德西特 (AdS) 时空中的弱非线性动力学，关注 AdS 不稳定性猜想，并专注于以简化形式准确捕获小初始数据的长期演化的共振近似。涵盖的主题包括湍流和规则运动、类似于振荡器链中的费米-帕斯塔-乌拉姆现象的动态重现，以及 AdS 动力学与谐波势中的非相对论非线性薛定谔方程之间的关系。特别提到弱非线性强共振系统的经典动力学通过相应量子理论中的微扰考虑来阐明的方式，特别是与量子混沌理论相关的方式。