地 点:理科楼 LD302
摘 要:It is well known that the constructions of space-filling curves depend on certain substitution rules. For a given self-similar set, finding such rules is somehow mysterious, and it is the main concern of the present paper. Our first idea is to introduce the notion of skeleton for a self-similar set. Then, from a skeleton, we construct several graphs, define edge-to-trail substitution rules, and explore conditions ensuring the rules lead to space-filling curves. Thirdly, we summarize the classical constructions of the space-filling curves into two classes: the traveling-trail class and the positive Euler-tour class. Finally, we propose a general Euler-tour method; using this method we show that if a self-similar set satisfies the open set condition and possesses a skeleton, then space-filling curves can be constructed. Especially, all connected self-similar sets of finite type fall into this class. Our study provides an algorithm to construct space-filling curves of self-similar sets.
报告人简介：张淑钦，奥地利莱奥本大学（University of Leoben）数学系博士，研究方向为分形几何，已在 《Nonlinearity》等杂志发表SCI论文数篇。