Quasisymmetric rigidity, carpet Julia sets and the landing of dynamical and parameter rays
Quasisymmetric rigidity, carpet Julia sets and the landing of dynamical and parameter rays
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发表时间：
2015-05
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通讯作者：
Jinsong Zeng
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作者：
Jinsong Zeng
本文共分五个部分。第一部分是关于一种新的Sierpinski地毯的准对称刚度，这不是准对称等价的标准Sierpinski地毯。第二部分讨论地毯Julia集的拟对称几何，包括一致拟圆和一致分离性。第三部分是确定多项式的两条外部射线何时落在同一点。作为应用，我们还证明了二次多项式族上核熵的单调性。在第四部分中，我们在崔和谭的工作基础上，利用经典的环模和准保形手术工具，研究了一些参数射线在平移轨迹参数空间中的着陆问题。最后一部分讨论了一类生成重整化变换。具体地说，是关于它的Julia集的连通性和它的参数空间中的非逃逸轨迹，以及Julia集的Hausdorff维数的渐近公式。
The thesis consists of five parts. The first part is concerned with the quasisymmetric rigidity of a new Sierpinski carpet, which are not quasis-ymmetrically equivalent to the standard Sierpinski carpets. The second part discusses the quasisymmetrically geometry of the carpet Julia sets, including the uniformly quasicircle and uniformly separated properties. The third part is to determine when two external rays of a polynomial land at the same point. As an application, we also show the monotonicity of core-entropy on a family of quadratic polynomials. In the fourth part, following Cui and Tan's work, we use the classic tools modulus of annulus and quasi-conformal surgery to study the landing of some parameter rays in shift locus parameter space. The last part discusses a family of generated renormal-ization transformations. Specifically, it is on the connec-tivity of its Julia sets and the non-escaping locus in its parameter space, the asymptotic formula of the Hausdorff dimention of the Julia sets.