The shape of Thurston's Master Teapot
The shape of Thurston's Master Teapot
复制标题
DOI：
10.1016/j.aim.2020.107481
复制
发表时间：
2019-02
影响因子：
1.7
通讯作者：
Harrison Bray;D. Davis;Kathryn A. Lindsey;Chenxi Wu
中科院分区：
文献类型：
--
作者：
Harrison Bray;D. Davis;Kathryn A. Lindsey;Chenxi Wu
我们建立了区间上单峰连续自映射的瑟斯顿主茶壶和瑟斯顿集的基本几何和拓扑性质。特别地，主茶壶是连通的，包含单位圆柱体，且它与集合D×{c}的交随c单调增长。我们证明了上述瑟斯顿集不等于后临界有限帐篷映射的瑟斯顿集，并给出了瑟斯顿集的有限逼近图中出现某些间隙的算术解释。
We establish basic geometric and topological properties of Thurston's Master Teapot and the Thurston set for superattracting unimodal continuous self-maps of intervals. In particular, the Master Teapot is connected, contains the unit cylinder, and its intersection with a set D×{c} grows monotonically with c. We show that the Thurston set described above is not equal to the Thurston set for postcritically finite tent maps, and we provide an arithmetic explanation for why certain gaps appear in plots of finite approximations of the Thurston set.