Dynamics of Newton maps
发布人: 曹思圆   发布时间: 2018-08-04   浏览次数: 22
报告人:王晓光(浙江大学,研究员,优青)

时间:8月7日(周二)9:30-10:30
地点:数学楼126
主持人:程涛


摘要:

    It is shown that the boundary $\partial B$ of any immediate root basin $B$ of $f$ is locally connected. Moreover, $\partial B$ is a Jordan curve if and only if ${\rm deg}(f|_B)=2$.  This implies that the boundaries of all components  of root basins, for all polynomials' Newton maps, from the viewpoint of topology, are tame.  This generalizes Roesch's groundbreaking work (Annals of Math. 2008) on cubic Newton maps to arbitrary degree.
   This work is joint with Yongcheng Yin and Jinsong Zeng.