學術報告

報告人：豐德軍教授（香港中文大學）

報告人簡介：豐德軍，香港中文大學教授。豐德軍教授在重分形分析、疊代函數系統的維數理論，熱力學機制的數學原理、自相似結構的剛性等研究上做出了一系列開創性的成果，在Comm. Pure Appl. Math., Geom. and Func. Anal., J. Eur. Math. Soc.等數學期刊上發表SCI論文50餘篇，引用700餘次，是國際分形幾何和動力系統研究領域的一流專家。

報告題目：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.

報告時間：2016年5月30日（星期一）下午3:30-4:30
報告地點：科技樓南樓702