学术报告

报告人：丰德军教授（香港中文大学）

报告人简介：丰德军，香港中文大学教授。丰德军教授在重分形分析、迭代函数系统的维数理论，热力学机制的数学原理、自相似结构的刚性等研究上做出了一系列开创性的成果，在Comm. Pure Appl. Math., Geom. and Func. Anal., J. Eur. Math. Soc.等数学期刊上发表SCI论文50余篇，引用700余次，是国际分形几何和动力系统研究领域的一流专家。

报告题目：Dimensions of projected sets and measures on self-affine sets

摘要：Let {ϕ_i (x)=T_i x+a_i }_(i=1)^l be an iterated function system on R^d consistingof contractive affine maps, and π∶ {1,…,l}^N→R^d the corresponding coding map.Under an additional assumption that ‖T_i ‖<1/2, for any given Borel set E and Borelprobability measure μ in the coding space, we determine the various dimensions of theirprojections under π for typical translations (a_1,…,a_l ); in particular, we give a necessaryand sufficient condition on μ so that the typical projection of μ is exactly dimensional.This extends the known results in the literature on typical projections of invariant setsand invariant measures. It plays an analogue to the (orthogonal) projection theorems ofHausdorff and packing dimensions. Further results are obtained for deterministic planarself-affine sets. The talk is partially based on joint work with Chiu-Hong Lo.

报告时间：2016年5月30日（星期一）下午3:30-4:30
报告地点：科技楼南楼702