Dynamics of sub-hyperbolic and semi-hyperbolic rational semigroups and skew products
Dynamics of sub-hyperbolic and semi-hyperbolic rational semigroups and skew products
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次双曲和半双曲有理半群及斜积的动力学
DOI：
10.1017/s0143385701001286
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发表时间：
2001
影响因子：
0.9
通讯作者：
Hiroki Sumi
中科院分区：
文献类型：
--
作者：
Hiroki Sumi
研究黎曼球上有理函数的亚双曲半群和半双曲半群的动力学问题，并给出一些无游荡域定理。一般的有理半群的Julia集合可以有非空的内点。给出了Julia集合没有内点的充分条件。从半群的前向和后向动力学的一些信息出发，我们考虑了Julia集合的面积等于零或Julia集合的Hausdorff维数的上估计。
We consider dynamics of sub-hyperbolic and semi-hyperbolic semigroups of rational functions on the Riemann sphere and will show some no wandering domain theorems. The Julia set of a rational semigroup in general may have non-empty interior points. We give a sufficient condition that the Julia set has no interior points. From some information about forward and backward dynamics of the semigroup, we consider when the area of the Julia set is equal to zero or an upper estimate of the Hausdorff dimension of the Julia set.