非自治动力系统纤维维数的正则性与非正则性
Regularity and irregularity of fiber dimension of non-autonomous dynamical systems
摘要：
本文研究了有理函数的非自治动力学，更确切地说，研究了非自治系统扰动下朱利亚集的分形行为.给出了参数空间上双曲型非自治朱利亚集关于$l^\infty$ -拓扑维数的Hölder连续性的全纯稳定性的一个充要条件.另一方面，我们表明，对于某些特定的家庭，Hausdorff和包装尺寸功能是不可微的，在任何一点上，这些尺寸是不相等的一个开放的密集集的参数空间仍然相对于$l^\infty$ -拓扑。
英文摘要：
This note concerns non-autonomous dynamics of rational functions and, more precisely, the fractal behavior of the Julia sets under perturbation of non-autonomous systems. We provide a necessary and sufficient condition for holomorphic stability which leads to Hölder continuity of dimensions of hyperbolic non-autonomous Julia sets with respect to the $l^\infty$-topology on the parameter space. On the other hand we show that, for some particular family, the Hausdorff and packing dimension functions are not differentiable at any point and that these dimensions are not equal on an open dense set of the parameter space still with respect to the $l^\infty$-topology.
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