论文标题
混沌式能量转移在哈密顿PDES中
Chaotic-like transfers of energy in Hamiltonian PDEs
论文作者
论文摘要
我们考虑在$ t^2 $上的非线性立方波，Hartree和非线性立方体束方程，我们证明存在不同类型的解决方案，这些解决方案在某些时间尺度中在傅立叶模式之间交换能量。可以将此交换视为\ emph {混沌样}，因为可以随机选择激活模式的选择或每个转移中所花费的时间。这些轨道的构建的关键是不变对象之间存在异斜连接与birkhoff正常形式的这些方程式截断的符号动力学（Smale Horseshoe）之间的杂节连接。
We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on $T^2$ and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange can be considered \emph{chaotic-like} since either the choice of activated modes or the time spent in each transfer can be chosen randomly. The key point of the construction of those orbits is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkhoff Normal Form truncation of those equations.
