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                                          • 天元讲堂03(1.6,1.8)​Stabilization of cycles: blender horseshoes, center-unstable Hénon-like families, and renormalization
                                          • 浏览量:10 发布人: 发布时间:2019-12-31
                                          • 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

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