The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on T2 exchanging energy among Fourier modes in a "chaotic-like" way. We say that a transition of energy is "chaotic-like" if either the choice of activated modes or the time spent in each transfer can be chosen randomly. We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations. The key point of the construction of the special solutions is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkhoff Normal Form of those equations.

中文翻译：

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哈密​​顿PDE中的混沌共振动力学和能量交换

本文的目的是在[16]中介绍最近的结果，其中我们以“类混沌”的​​方式提供了在傅立叶模式之间的T2交换能量上一些非线性共振PDE的解。我们说，如果可以随机选择激活模式的选择或每次传输所花费的时间，则能量的转换类似于“混沌”。我们考虑了非线性三次波，Hartree和非线性三次梁方程。构造特殊解的关键是不变对象之间存在异质连接，以及这些方程的Birkhoff范式的符号动力学（Smale马蹄形）的构造。