摘要:Given $lain(0, 1)$, let $E_la$ be the self-similar set generated by the iterated function system ${x/3,(x+la)/3,(x+2)/3}$. Then $E_la$ is a self-similar set with overlaps. We obtain the sufficient and necessary {condition} for $E_la$ to be {it totally self similar}, which is a concept first introduced by Broomhead, Montaldi, and

Sidorov in 2004. When $E_la$ is totally self-similar, all its generating IFSs are investigated, and the size of the set of points having finite triadic codings is determined. Besides, we give some properties of the spectrum of $E_la$ and show that the spectrum of $E_la$ vanishes if and only if $la$ is irrational.

报告人：姚媛媛副教授 华东理工大学

简介：姚媛媛副教授研究方向为分形几何，发表SCI论文十余篇，曾主持国家自然科学基金青年基金等，并多次获得华东理工大学教学奖项。

报告时间：2018年11月24日（星期六）16:00—16:50

报告地点：数学科学学院38号楼110

主办单位：数学科学学院

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