论文标题
部分可观测时空混沌系统的无模型预测
On the abundance of $k$-fold semi-monotone minimal sets in bimodal circle maps
论文作者
论文摘要
受到马瑟（Mather）的扭曲映射定理的启发，我们研究了经常性不变式集合，这些套件像刚性旋转一样在双峰圆形地图$ g $ $ g $ to $ k $ fold封面的作用下进行订购。对于旋转内部的每个不合理的，$ k $折叠的订购的半折叠式最小设置的集合与该旋转数字中包含$（k-1）$ - 尺寸 - 弱拓扑中的尺寸球。我们还完全描述了它们用于合理旋转数字的周期性轨道类似物。主要工具是对Hedlund和Morse的构造的概括，该构建产生了这些$ K $折叠良好的不变式套件的象征类似物。
Inspired by a twist maps theorem of Mather we study recurrent invariant sets that are ordered like rigid rotation under the action of the lift of a bimodal circle map $g$ to the $k$-fold cover. For each irrational in the interior of the rotation set the collection of the $k$-fold ordered semi-Denjoy minimal sets with that rotation number contains a $(k-1)$-dimensional ball in the weak topology on their unique invariant measures. We also describe completely their periodic orbit analogs for rational rotation numbers. The main tool is a generalization of a construction of Hedlund and Morse which generates the symbolic analogs of these $k$-fold well-ordered invariant sets.
