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Proof of the Branner-Hubbard conjecture on Cantor Julia sets 被引量:8
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作者 QIU WeiYuan yin yongcheng 《Science China Mathematics》 SCIE 2009年第1期45-65,共21页
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... 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. 展开更多
关键词 Julia set Branner-Hubbard conjecture PUZZLE TABLEAU 37F10 37F20
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GEOMETRY AND DIMENSION OF SELF-SIMILAR SET 被引量:2
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作者 yin yongcheng JIANG HAIYI SUN YESHUN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2003年第1期57-64,共8页
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 tha... 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. 展开更多
关键词 Self-similar set Uniformly perfect set Hausdorff dimension
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THE TOPOLOGY OF JULIA SETS FOR GEOMETRICALLY FINITE POLYNOMIALS 被引量:1
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作者 yin yongcheng 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1998年第1期77-80,共4页
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... 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. Hubbard partially. 展开更多
关键词 Filled-in Julia set Geometrically finite polynomial TOPOLOGY
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