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                        • 天元講堂03(1.6,1.8)?Stabilization of cycles: blender horseshoes, center-unstable Hénon-like families, and renormalization
                        • 瀏覽量:10 發布人: 發布時間:2019-12-31
                        • 題目  Stabilization of cycles: blender horseshoes, center-unstable Hénon-like families, and renormalization: Part I
                          報告人:Lorenzo Diaz(Catholic University of Rio de Janeiro (PUC)
                          時間  2020年1月6日 10:00-12:00

                          地點   精正樓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.



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

                          地點   精正樓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.


                          邀請人:楊大偉

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