科学研究
学术报告

Dimension estimates for C^1 iterated function systems

发布时间:2024-04-22 作者: 浏览次数:
Speaker: 丰德军 DateTime: 2024年4月29日(周一)下午16:00-17:00
Brief Introduction to Speaker:

丰德军,香港中文大学教授,国内外分形几何,遍历理论与动力系统等研究方向的知名专家。他在重分形分析、迭代函数系统的维数理论、伯努利卷积、动力系统压力函数性质及变分原理、随机覆盖、Pisot数的算术性质、自相似集的仿射嵌入等方面取得大量重要的研究成果。这些成果发表在Duke Math. J.,  Adv. Math., Ann.Probab.,Comm. Pure Appl. Math.,Geom. Funct. Anal., J. Eur. Math. Soc.,J. Math. Pures Appl.等国际数学界重要期刊上。丰德军教授与内地,法国、美国、芬兰、日本、阿根廷等多个国家的专家学者有着密切联系与合作,多次应邀在国际学术会议上做报告并组织相关国际学术会议。

Place: 6号楼2楼报告厅
Abstract: In this talk, we consider dimensional properties of the attractors of nonlinear and nonconformal iterated function systems (IFS) on R^d. We introduce a generalized transversality condition (GTC) for parameterized families of C^1 IFSs, and show that if the GTC is satisfied, then the Hausdorff and box-counting dimensions of the attractor of a typical IFS are given by the singularity dimension. Moreover, we verify the GTC for some parametrized families of C^1 IFSs. This is based on joint work with Karoly Simon.