关于共形推斥器的尺寸。随机性和参数依赖性
On the dimensions of conformal repellers. Randomness and parameter dependency
摘要：
鲍文公式将共形反射极的豪斯多夫维数与“压力”函数的零点联系起来。我们提出了一个基本的，自足的证明，绕过测度论和热力学形式主义表明，鲍文公式适用于$C^1$共形排斥。我们认为时间相关的共形排斥作为一个合适的类内的共形扩展映射序列的不变子集。我们表明，鲍文公式推广到这样的一个排斥，如果该序列是随机挑选的，那么豪斯多夫维数的排斥几乎肯定同意其上，下盒尺寸，并给出了一个自然的推广鲍文公式。对于黎曼球面上的随机一致双曲朱利亚集，我们证明了如果映射族和概率律实解析地依赖于参数，那么它的几乎几乎必然豪斯多夫维数也是如此.
英文摘要：
Bowen's formula relates the Hausdorff dimension of a conformal repeller to the zero of a `pressure' function. We present an elementary, self-contained proof which bypasses measure theory and the Thermodynamic Formalism to show that Bowen's formula holds for $C^1$ conformal repellers. We consider time-dependent conformal repellers obtained as invariant subsets for sequences of conformally expanding maps within a suitable class. We show that Bowen's formula generalizes to such a repeller and that if the sequence is picked at random then the Hausdorff dimension of the repeller almost surely agrees with its upper and lower Box dimensions and is given by a natural generalization of Bowen's formula. For a random uniformly hyperbolic Julia set on the Riemann sphere we show that if the family of maps and the probability law depend real-analytically on parameters then so does its almost sure Hausdorff dimension.
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