报告题目：On fair entropy of the tent family

报告人：高睿，四川大学

时间：2021年7月8日（周四）下午 15:00开始

地点：东区管理科研楼1418教室

摘要： In this talk, we begin with recalling the notions of fair measure and fair entropy introduced by Misiurewicz and Rodrigues recently.  Then we focus on fair entropy $h(a)$ of the tent map $f_a$ with slope $a$ and study its regularity as a function of the parameter $a$. We show that $h$ is $\frac{1}{2}$-Hölder continuous on $[\sqrt{2},2]$ and identify its best Hölder exponent on each subinterval of $[\sqrt{2},2]$. We also establish a formula of pointwise Hölder exponents of $h$ at parameters chosen in a set of full Lebesgue measure, which particularly implies that the derivative of $h$ vanishes almost everywhere. This talk is based on a joint work with Bing Gao.

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