Core entropy and biaccessibility of quadratic polynomials
Core entropy and biaccessibility of quadratic polynomials
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发表时间：
2014-01
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通讯作者：
W. Jung
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作者：
W. Jung
对于复二次多项式，通过考虑双入角的Hausdorff维和核熵：Hubbard树上的拓扑熵，从另一个角度理解了Julia集的拓扑和动力学。根据瑟斯顿的说法，这些量是相关的。Tiozzo[arxiv：1305.3542]在Mandelbrot集M的主脉上表现出连续性。这一结果被推广到这里的所有静脉，并且它表明相对于外角θ的连续性将意味着参数c的连续性。描述了与重整化相关的双可及维度的水平集。找到了有理角度的H“老渐近性，证实了Bruin-Schleicher给出的H”老指数[arxiv：1205.2544]。还得到了在并矢角下局部极大值的部分结果，并提出了维度作为外角的函数的可能的自相似性。
For complex quadratic polynomials, the topology of the Julia set and the dynamics are understood from another perspective by considering the Hausdorff dimension of biaccessing angles and the core entropy: the topological entropy on the Hubbard tree. These quantities are related according to Thurston. Tiozzo [arXiv:1305.3542] has shown continuity on principal veins of the Mandelbrot set M . This result is extended to all veins here, and it is shown that continuity with respect to the external angle theta will imply continuity in the parameter c . Level sets of the biaccessibility dimension are described, which are related to renormalization. H\"older asymptotics at rational angles are found, confirming the H\"older exponent given by Bruin--Schleicher [arXiv:1205.2544]. Partial results towards local maxima at dyadic angles are obtained as well, and a possible self-similarity of the dimension as a function of the external angle is suggested.