题目  Stabilization of cycles: blender horseshoes, center-unstable Hénon-like families, and renormalization: Part I
报告人：Lorenzo Diaz（Catholic University of Rio de Janeiro (PUC)) 
时间  2020年1月6日 10:00-12:00

地点   精正楼307


摘要   We discuss the (hetedimensional) cycles stabilization problem. For that we introduce robust cycles and explain how the stabilization of a cycle depends on the degree of 

differentiability considered. We close the first part by summarizing some results in the $C^1$-topology which depend on the notion of a blender horseshoe.



题目  Stabilization of cycles: blender horseshoes, center-unstable Hénon-like families, and renormalization: Part II
报告人：Lorenzo Diaz（Catholic University of Rio de Janeiro (PUC)) 
时间  2020年1月8日 10:00-12:00

地点   精正楼307


摘要  The next step is to discuss the stabilization problem in higher differentiability settings focusing on the so-called heterodimensional tangencies. The main steps is to see that center-unstable Hénon-like families yield blender horseshoes and that these families appear as limit families of some 
heterodimensional cycles with heterodimensional tangencies. Finally, we present a setting where the stabilization of cycles is obtained. The general principle is that we can obtain $C^2$-stabilization of cycles by adding geometrical complexity to the cycles.

In this talk we will explain all ingredients considered: heterodimensional cycles, heterodimensional tangencies, robust cycles, blender horseshoes, center-unstable Hénon-like families, and renormalization.


邀请人：杨大伟