标题： 扰动连续映射在康托尔集上的相图的灵活性与通用性 显示英文标题

标题： Flexibility versus genericity of phase diagrams of perturbed continuous maps on the Cantor set

摘要： 考虑由连续函数$F:\mathcal{A}^\mathbb{N}\to\mathcal{A}^\mathbb{N}$构成的动力系统，其中$\mathcal{A}$是一个有限字母表。扰动的对应物，记为$F_\epsilon$，在每次迭代$F$后通过以概率$\epsilon\in[0,1]$独立地修改每个单元，并选择新的值均匀进行得到。我们描述可能的$\epsilon\in[0,1]$集合，使得$F_\epsilon$有一个唯一的测度。 这些集合正是$G_\delta$集（开集的可数交集）属于$[0, 1]$，其中包含1。 然而，我们证明通常情况下这个集合是$]0, 1]$。 显示英文摘要

摘要： Consider the dynamical system constitued by a continuous function $F:\mathcal{A}^\mathbb{N}\to\mathcal{A}^\mathbb{N}$ where $\mathcal{A}$ is a finite alphabet. The perturbed counterpart, denoted by $F_\epsilon$, is obtained after each iteration of $F$ by modifying each cell independently with probability $\epsilon\in[0,1]$ and choosing the new value uniformly. We characterize the possible sets of $\epsilon\in[0,1]$ such that $F_\epsilon$ has a unique measure. These sets are exactly the $G_\delta$ sets (countable intersection of open sets) of $[0, 1]$ which contain 1. However, we show that generically this set is $]0, 1]$.