尹永成 照片

尹永成

教授 博士生导师

所属大学: 浙江大学

所属学院: 数学科学学院

邮箱:
yin@zju.edu.cn

个人主页:
https://person.zju.edu.cn/ycyin

个人简介

1981.9-1985.7,复旦大学数学系,本科生;

1985.9-1988.7,复旦大学数学所,硕士研究生;

1988.9-1991.7,复旦大学数学所,博士研究生;

1991.8-1993.7,浙江大学高等数学研究所,博士后;

1993.8-2007.8,浙江大学教师;

2007.9-2011.2, 复旦大学教师;

2011.3-现在,浙江大学教师;

1994.12,副教授;

1998.7,教授。

教学与课程

近年主讲课程:

1、数学分析(甲),数学求是科学班;

2、复变函数,数学求是科学班;

3、复分析,数学学院专业选修课。

科研

承担的国家自然科学基金项目:

1、抛物和Cremer有理函数的拓扑动力学,1995.01~1997.12;

2、经典复分析(“九五”重点成员),1996.01 ~2001.12;

3、共形几何中的若干问题及其应用,2002.01 ~2004.12;

4、复动力系统与拟共形映射(“十五”重点成员),2003.01~2006.12;

5、解析函数的迭代理论,2007.01~2009.12;

6、复动力系统若干问题研究(“十一五”重点成员),2009.01~2012.12;

7、复动力系统及其应用(“十二五”重点成员),2013.1~2017.12;

8、有理函数参数空间的拓扑性质,2018.1~2021.12.

研究与成果

研究一维复动力系统中的拓扑问题,取得以下主要研究成果:

给出多项式Julia集为Cantor集的充分必要条件,解决了Branner-Hubbard猜想;

证明了多项式有界吸引和抛物Fatou区域是Jordan区域;

证明了Devaney关于McMullen函数族在动力系统平面和参数空间的猜想;

证明多项式Newton迭代映射吸引Fatou区域的边界的局部连通性。

研究领域

复动力系统

近期论文

P. Roesch and Y. Yin, The boundary of bounded polynomial Fatou components, C R Acad Sci Paris Ser I., 346(2008), no.15-16, 877-880.

W. Qiu and Y. Yin, Proof of the Branner-Hubbard conjecture on Cantor Julia set, Science in China, Vol.52, No.1(2009), 45-65.

Y. Yin and Y. Zhai, No invariant line fields on Cantor Julia sets, Forum Mathematicum, 22(2010), No.1, 75-94.

J. Qiao, Y. Yin and J. Gao, Feigenbaum Julia sets of Yang-Lee zeros, Ergodic Theory and Dynamical Systems, 30(2010), 1573-1591.

X. Wang, W. Qiu, Y. Yin, J. Qiao and J. Gao, Connectivity of the Mandelbrot set for the family of renormalization transformations, Science in China, Ser.A, 53(2010), 849-862

W. Peng, W. Qiu, P. Roesch, L. Tan and Y. Yin, A tableau appproach of the KSS nest, Conformal geometry and dynamics(AMS electronic journal), 14(2010), 35-67.

X. Wang, W. Qiu, Y. Yin, Local connectivity of Julia sets: McMullen maps, Adv. in Math., 229(2012), 2525-2577.

W. Peng, Y. Yin and Y. Zhai, On the quasiconformal surgery of rational maps with Cantor Julia sets, Ergodic Theory and Dynamical Systems, 32(2012), 1711-1726.

W. Qiu, Y. Xiao, and Y. Yin, On dynamics of generalized McMullen maps, Ergodic Theory and Dynamical Systems, 34(2014), 2093-2112.

W. Qiu, F. Yang, and Y. Yin, Rational maps whose Juia sets are Cantor circles, Ergodic Theory and Dynamical Systems, 35(2015), 499-529.

W. Qiu, P. Roesch, X. Wang and Y. Yin, Hyperbolic components of McMullen maps, Annales de l’ENS, 48(2015), 703-737.

W. Qiu, F. Yang, and Y. Yin, Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps, Discrete and Continuous Dynamical Systems-A, Vol.36, No.6, 2016, 3375-3416.

X. Wang and Y. Yin, Global topology of hyperbolic components: Cantor circle case, Proc. of LMS, 2017, 115(4), 897-923.

P. Roesch, X. Wang and Y. Yin, Moduli space of cubic Newton maps, Adv. Math., 322(2017), 1-59.

W. Qiu, F. Yang and Y. Yin, Quasisymmetric geometry of the Julia sets of McMullen maps, SCIENCE CHINA Mathematics, 2018.

预印本:

P. Roesch and Y. Yin, The boundary of bounded critical Fatou components for polynomials. pdf

W.Wang, Y.Yin and J.Zeng, Dynamics of Newton maps, 2018.