Kuramoto-Sivashinsky动力学中的不稳定递归斑图
Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics
摘要：
我们进行了系统的探索经常性的模式在1维Kuramoto-Sivashinsky系统。对于一个小的，但已经相当动荡的系统，长时间的动力学发生在一个低维不变流形。一组平衡提供了这个流形的一个粗略的几何划分。变分方法使我们能够确定大量的数值不稳定的时空周期解。吸引集似乎令人惊讶地薄-它的骨干是几个斯梅尔马蹄排斥，很好地近似的内在局部1维返回映射，每个近似的符号动力学。动力学似乎分解成混沌动力学在这样的本地排斥，穿插在它们之间的快速跳跃。
英文摘要：
We undertake a systematic exploration of recurrent patterns in a 1-dimensional Kuramoto-Sivashinsky system. For a small, but already rather turbulent system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set of equilibria offers a coarse geometrical partition of this manifold. A variational method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions. The attracting set appears surprisingly thin - its backbone are several Smale horseshoe repellers, well approximated by intrinsic local 1-dimensional return maps, each with an approximate symbolic dynamics. The dynamics appears decomposable into chaotic dynamics within such local repellers, interspersed by rapid jumps between them.
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