07-08【高 睿】管楼1418 吴文俊数学重点实验室Dynamical Systems Seminar

发布者:万宏艳发布时间:2021-07-06浏览次数:11

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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