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THE TOPOLOGY OF JULIA SETS FOR GEOMETRICALLY FINITE POLYNOMIALS

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Chinese Annals of Mathematics,Series B 1998年第1期19卷 77-80页

作者： yin yongcheng 浙江大学数学所浙江杭州

By means of the Branner-Hubbard puzzle, the author studies the topology of filled-in Julia sets for geometrically finite polynomials,and proves a conjecture of C. McMullen and a conjecture of B. Branner and J. H. Hu... 详细信息

关键词： Filled-in Julia set Geometrically finite polynomial Topology

Bounded critical Fatou components are Jordan domains for polynomials

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Science China Mathematics 2022年第2期65卷 331-358页

作者： Pascale Roesch yongcheng yin Institut de Mathematiques de Toulouse Universite Paul SabatierToulouse 31062France School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China

We prove that any bounded Fatou component of a polynomial of degree at least two, which is not(eventually) a Siegel disk, is a Jordan domain.

关键词： Fatou component Jordan domain puzzle local connectivity

Uniform perfectness of the attractor of bi-Lipschitz IFS

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Science China Mathematics 2006年第4期49卷 433-438页

作者： RUAN Huojun SUN Yeshun yin yongcheng Department of Mathematics Zhejiang University Hangzhou 310027 China Department of Mathematics Zhejiang University Hangzhou 310027 China Department of Mathematics Zhejiang University Hangzhou 310027 China

In this paper, we prove that the attractor of C1,a bi-Lipschitz IFS in R is uniformly perfect if it is not a singleton. Then we construct an example to show that this does not hold for C1 bi-Lipschitz IFS in Rn.

关键词： uniform perfectness, iterated function systems.

Proof of the Branner-Hubbard conjecture on Cantor Julia sets

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Science China Mathematics 2009年第1期52卷 45-65页

作者： QIU WeiYuan yin yongcheng School of Mathematical Sciences Fudan UniversityShanghai 200433China

By means of a nested sequence of some critical pieces constructed by Kozlovski, Shen, and van Strien, and by using a covering lemma recently proved by Kahn and Lyubich, we prove that a component of the filled-in Julia set of any polynomial is a point if and only if its forward orbit contains no periodic critical components. It follows immediately that the Julia set of a polynomial is a Cantor set if and only if each critical component of the filled-in Julia set is aperiodic. This result was a conjecture raised by Branner and Hubbard in 1992.

关键词： Julia set Branner-Hubbard conjecture puzzle tableau 37F10 37F20

GEOMETRY AND DIMENSION OF SELF-SIMILAR SET

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Chinese Annals of Mathematics,Series B 2003年第1期24卷 57-64页

作者： yin yongcheng JIANG HAIYI SUN YESHUN Department of Mathematics Zhejiang University Hangzhou 310027 China.Department of Mathematics Zhejiang University Hangzhou 310027 China.Department of Mathematics Zhejiang University Hangzhou 310027 China.

The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case that it is a singleton. As a corollary, it is proved that this self-similar set has positive Hausdorff dimension provided that it is not a singleton. And a lower bound of the upper box dimension of the uniformly perfect sets is given. Meanwhile the uniformly perfect set with Hausdorff measure zero in its Hausdorff dimension is given.

关键词： Self-similar set Uniformly perfect set Hausdorff dimension

Quasisymmetric geometry of the Julia sets of McMullen maps Dedicated to the Memory of Professor Lei Tan

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Science China Mathematics 2018年第12期61卷 2283-2298页

作者： Weiyuan Qiu Fei Yang yongcheng yin School of Mathematical Sciences Fudan University Department of Mathematics Nanjing University School of Mathematical Sciences Zhejiang University

We study the quasisymmetric geometry of the Julia sets of McMullen maps f_λ(z) = z^m+ λ/z~?,where λ∈ C \ {0} and ? and m are positive integers satisfying 1/? + 1/m < 1. If the free critical points of f_λ are escaped to the infinity, we prove that the Julia set J_λ of f_λ is quasisymmetrically equivalent to either a standard Cantor set, a standard Cantor set of circles or a round Sierpiński carpet(which is also standard in some sense).If the free critical points are not escaped, we give a sufficient condition on λ such that J_λ is a Sierpiński carpet and prove that most of them are quasisymmetrically equivalent to some round carpets. In particular, there exist infinitely renormalizable rational maps whose Julia sets are quasisymmetrically equivalent to the round carpets.

关键词： Julia sets Sierpiński carpet quasisymmetrically equivalent

SOME DYNAMICAL PROPERTIESOF QUADRATIC RATIONAL MAPS

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Chinese Annals of Mathematics,Series B 1994年第3期15卷 373-384页

作者： yin yongcheng(Celltre for Mathematical Sciences, Zhejiang Universityt HangZhou 310027, Zhejiallg, China.) ZHEJIANG UNIV CTR MATH SCIHANGZHOU 310027PEOPLES R CHINA

This paper studies the dynamics of the analytic family z + 1/z + b alld describes the topologyof the parameter space, structural stability and J-stability. The mapping class group of almostall maps of the above family... 详细信息

关键词： Complex dyllamics Julia set Structural stability J-stability Mapping class group.

Connectivity of the Mandelbrot set for the family of renormalization transformations

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Science China Mathematics 2010年第3期53卷 849-862页

作者： WANG XiaoGuang 1,QIU WeiYuan 1 , yin yongcheng 1 , QIAO JianYong 2 & GAO JunYang 2 1 School of Mathematical Sciences, Fudan University, Shanghai 200433, China 2 Center of Mathematics, China University of Mining and Technology, Beijing 100083, China School of Mathematical Sciences Fudan University Shanghai China Center of Mathematics China University of Mining and Technology Beijing China

We show that the Mandelbrot set for the family of renormalization transformations of 2-dimensional diamond-like hierachical Potts models in statistical mechanics is connected. We also give an upper bound for the Hausd... 详细信息

关键词： connectivity Mandelbrot set renormalization transformations

Wearable ultrasensitive and rapid human physiological monitoring based on microfiber Sagnac interferometer

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Science China(Information Sciences) 2024年第3期67卷 281-290页

作者： Xin WANG Hongyou ZHOU Meihua CHEN yongcheng HE Zhishen ZHANG Jiulin GAN Zhongmin YANG State Key Laboratory Luminescent Materials and Devices Institute of Optical Communication MaterialsSpecial Glass Fiber and Device Engineering Technology Research and Development Center of Guangdong ProvinceGuangdong Provincial Key Laboratory of Fiber Laser Materials and Applied TechniquesSouth China University of Technology Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology Foshan University

High-sensitive and fast-responding flexible strain sensors are essential for the smart wearable devices that precisely and dynamically perceive the weak deformations induced by human physiological signals. Here, a flexible strain sensor via polydimethylsiloxane(PDMS)-encapsulated microfiber Sagnac interferometer was designed and prepared for monitoring the human pulse signals and sound vibrations. The sensor achieved a record-breaking sensitivity(gauge factor, GF = 9977) and an extremely low detection limit(0.00025%) due to the strong polarization-dependent coupling effect in the microfiber coupler and the polarization-mixing effect in the Sagnac loop. The relative intensity demodulation method also enabled a fast response time of 10 μs. The wearable pulse measurements were implemented by attaching this flexible strain sensor directly to human skin at various locations and the waveform details were accurately captured. Taking advantage of the ultra-high sensitivity and fast response performance of the prepared sensor, the real-time dynamic acquisition of the underwater weak signal, such as the hydro-acoustic waves with a wide range of 20 Hz–16.86 k Hz, has been demonstrated. These initial results pave the way for a new and innovative category of underwater wearable devices with rapid detection of human physiological signals and weak environmental vibrations.

关键词： flexible strain sensor microfiber Sagnac interferometer underwater detection