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数学学院 、所系列学术报告(708场):南开大学马王俭教授

admin 发表于: 2017-06-14 09:15  点击:320

   目:The rigidity of irrational pseudo-rotations on the two-torus

    人:南开大学 王俭教授

   间:20170615 下午2:30-3:30 

   点:数学楼一楼报告厅

 

  

In this talk, we give some sufficient conditions for the  $C^{r-1}$-rigidity of the $C^r$ conservative irrational pseudo-rotations on $mathbb{T}^2$.  When $f$ is a $C^r$ conservative super-Liouvillean pseudo-rotation on $mathbb{T}^2$,  we prove that $f$ is $C^{r-1}$-rigid if $f$  satisfies the bounded mean motion. When the rotation set of $f$ is semi-irrational vector, we define the strong non-Brjuno type  which includes the semi-irrational super-Liouvillean vectors. If the rotation set of $f$ is the strong non-Brjuno type, under a weaker bounded condition, we prove that $f$ is $C^{r-1}$-rigid.   Furthermore, we construct a $C^infty$ conservative (resp. minimal)  totally irrational pseudo-rotation with a super-Liouvillean vector and bounded mean motion that is not conjugate to an irrational rotation by the classical Anosov-Katok method.  Combining with a theorem of Jager, we give a negative answer to a long standing question of A. Norton and D. Sullivan in the $C^{infty}$ category.