报告人： 何宝林，上海师范大学
报告时间：2017年3月1日 10:15-12:00
地点：维格堂319
 摘要: For diffeomorphisms of line, we set up the identity between their length growth rate and their entropy. Then, we prove that there is $C^0$-open and $C^r$-dense subset $/u$ of $/Diff^r (/r)$ with bounded first-order derivative, $r=1,2,/cdots$, $+/infty$, such that the entropy map with respect to strong $C^0$-topology is continuous on $/u$; moreover, for any $f /in /u$, if it is uniformly expanding or $h(f)=0$, then the entropy map is locally constant at $f$.Also, we construct two examples://1. there exists open subset $/u$ of $/Diff^{/infty} (/r)$ such that the entropy map with respect to strong $C^{/infty}$-topology, is not locally constant at every map in $/u$.//2. there exists $f /in /Diff^{/infty}(/r)$ such that the entropy map with respect to strong $C^{/infty}$-topology, is neither lower semi-continuous nor upper semi-continuous at $f$.