标题： 实直线上解析自共形集的指数分离 显示英文标题

标题： On exponential separation of analytic self-conformal sets on the real line

摘要： 在最近的一篇文章中，Rapaport 表明实线上指数分离的解析 IFS 没有维数下降。 我们表明，在解析 IFS 的空间中，这样的指数分离 IFS 的集合在$\mathcal{C}^2$拓扑中包含一个开且稠密的集合。 此外，我们给出了 IFS 指数分离的一个充分条件，使我们能够构造出显式的指数分离例子。 关键的技术工具是引入了\textit{对偶 IFS}，我们认为它本身就有重要的研究价值。 作为应用，我们还刻画了何时一个解析 IFS 可以共轭为自相似 IFS。 显示英文摘要

摘要： In a recent article, Rapaport showed that the there is no dimension drop for exponentially separated analytic IFSs on the real line. We show that the set of such exponentially separated IFSs in the space of analytic IFSs contains an open and dense set in the $\mathcal{C}^2$ topology. Moreover, we give a sufficient condition for the IFS to be exponentially separated which allows us to construct explicit examples which are exponentially separated. The key technical tool is the introduction of the \textit{dual IFS} which we believe has significant interest in its own right. As an application we also characterise when an analytic IFS can be conjugated to a self-similar IFS.