Title1: Two problems on fractal necklces

Speaker: Prof. Shengyou Wen ( Hubei University )

Time: Fri,  Nov.20 2020, PM: 15:00-15:50

Title2: Quasisymmetrically equivalence of the sets defined by matrix restrictions

Speaker: Prof. Chun Wei ( Zhongnan University of Economics and Law)

Time: Fri,  Nov.20 2020, PM: 15:50-16:40

Title3: On the entropy of beta-expansion of real numbers

Speaker: Dr. Yuanyang Chang ( Wuhan University of Technology)

Time: Fri,  Nov.20 2020, PM: 16:40-17:30

Location:  4224, Building No.4, Wushan Campus

Inviter: Prof. Bing Li

Abstract 1：

       In this talk, the following two problems on fractal necklaces are discussed.  

       Problem 1. Does every fractal necklace satisfy the open set condition?  

       Problem 2. Does every stable self-similar necklace has no cut points?

Abstract 2：

     We study the geometric structure of the sets defined by matrix restrictions, give a necessary and sufficient condition which can characterize when the sets defined by matrix restrictions are quasisymmetrically equivalent.

Abstract 3：

        Let beta>1 be a real number. We consider the entropy of beta-expansion of real numbers in the unit interval, which is defined as the logarithmic growth rate of the beta-expansion. The Hausdorff dimension of the level sets of entropy is determined. If time admitted, we shall also show some attempts to determine the size of the intersection of two level set of entropy in two different bases. This is an ongoing joint work with Prof. Bing Li.