中科院数学与系统科学研究院
数学研究所
动力系统研讨班
报告人：杨飞 副教授（南京大学）
题 目：Self-similarity of high type Siegel disk boundaries in the quadratic family
时 间：2021.12.09（星期四），10:00-11:00
地 点：腾讯会议 996 451 300
摘 要：In 1998, McMullen proved that the Siegel disk boundaries of quadratic polynomials are self-similar provided the rotation numbers are of quadratic irrational. In this talk, we discuss the self-similarity for a certain general case. Let f be a map in the invariant class of Inou and Shishikura such that f has an irrational fixed point at the origin with rotation number $\alpha$. We prove that the boundary of the Siegel disk of f is self-similar at the critical point if $\alpha$ is of bounded type and of high type. In particular, this result can be applied to the quadratic polynomials, some exponential maps and the sine family. This talk is based on a joint work with Arnaud Chéritat.
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报告人：曾劲松 副教授（广州大学）
题 目：Decomposition of rational maps
时 间：2021.12.13（星期一），10:00-11:00
地 点：腾讯会议 898 661 012
摘 要：This talk is mainly about the dynamics of rational maps on the Riemann sphere. We will show that every postcritically finite rational map with non-empty Fatou set can be decomposed into bubble rational maps and Sierpinski rational maps. Based on this theory, an invariant and finite connected graph can be constructed in the Julia set. This is a joint work with Guizhen Cui and Yan Gao.
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