Shrinking Target Problem for Matrix Transformations of Tori

Abstract

The shrinking target problem concerns the sizes of the sets of the points in a metric space whose orbits under a transformation fall into a family of shrinking subsets infinitely often. We study such problems for matrices with real coefficients which are transformations on the d-dimensional torus. We obtain a zero-one law for the Lebesgue measure of the corresponding shrinking target sets. A Hausdorff dimension formula is also given for the diagonal matrix transformations. This is a joint work with Bing Li, Sanju Velani and Evgeniy Zorin.

Speaker

廖灵敏，2008年获得法国Picardie大学及武汉大学博士学位。2010年获得法国东巴黎大学终身教职。2017年获Habilitation。2022年7月起任武汉大学教授、博士生导师。主要从事分形几何，动力系统，度量数论等方面的研究。连续三次获得法国教育部A级优秀科研奖励(PEDR)。