论文标题
混乱的谐振动力和哈密顿PDE的能源交流
Chaotic Resonant Dynamics and Exchanges of Energy in Hamiltonian PDEs
论文作者
论文摘要
本说明的目的是在[16]中介绍最新结果，在该结果中，我们在\ emph {chaotic-like}方式中提供了一些非线性谐振PDE的解决方案。我们说，如果可以随机选择活化模式或每种转移中所花费的时间，则能量的过渡是\ emph {混乱的}。我们考虑非线性立方波，哈特里和非线性立方束方程。特殊解决方案构建的关键点是对这些方程的Birkhoff正常形式的不变对象与符号动力学（Smale Horseshoe）之间的杂节连接存在。
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 the 2-dimensional torus exchanging energy among Fourier modes in a \emph{chaotic-like} way. We say that a transition of energy is \emph{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.
