Topological conjugacy for unimodal nonautonomous discrete dynamical systems

Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries

Let $\{f_t\colon I\to I\}$ be a family of unimodal maps with topological entropies $h(f_t)>\frac12\log 2$, and ${\widehat{f}}_t\colon{\widehat{I}}_t\to{\widehat{I}}_t$ be their natural extensions, where ${\widehat{I}}_t=\varprojlim(I,f_t)$. Subject to some regularity conditions, which are satisfied by tent maps and quadratic maps, we give a complete description of the prime ends of the Barge-Martin embeddings of ${\widehat{I}}_t$ into the sphere. We also construct a family $\{χ_t\colon S^2\to S^2\}$ of sphere homeomorphisms with the property that each $χ_t$ is a factor of ${\widehat{f}}_t$, by…

一维动力学中周期点的乘子

The multipliers of periodic points in one-dimensional dynamics

将证明，不具有周期吸引子和康托吸引子的$S-$单模映射的光滑共轭类由周期轨道的乘子确定。这推广了M.Shub和D.Sullivan关于圆的光滑扩张映射的一个结果。

Embedding Information onto a Dynamical System

The celebrated Takens' embedding theorem concerns embedding an attractor of a dynamical system in a Euclidean space of appropriate dimension through a generic delay-observation map. The embedding also establishes a topological conjugacy. In this paper, we show how an arbitrary sequence can be mapped into another space as an attractive solution of a nonautonomous dynamical system. Such mapping also entails a topological conjugacy and an embedding between the sequence and the attractive solution spaces. This result is not a generalization of Takens embedding theorem but helps us understand what …

布劳尔复形的应用：洗牌、排列统计和动力系统

Applications of the Brauer complex: card shuffling, permutation statistics, and dynamical systems

利用代数群理论，给出了从有限群的半单共轭类到外尔群的共轭类的映射.随机一致选取一个半单类，得到外尔群共轭类的一个概率测度。利用Brauer复形，证明了该测度与Cellini利用仿射外尔群构造的外尔群的共轭类的第二测度一致.给出了$A$型的Cellini测度公式，从而导出了洗牌的新模型，并具有有趣的组合和数论结果。C型分析给出了动力系统中Rogers问题的另一种解决方案：用循环结构计数单峰置换。证明使用了有限域上回文多项式的因式分解理论。联系与对称函数理论。