POROSITY OF JULIA SETS OF NON-RECURRENT AND PARABOLIC COLLET{ECKMANN RATIONAL FUNCTIONS
POROSITY OF JULIA SETS OF NON-RECURRENT AND PARABOLIC COLLET{ECKMANN RATIONAL FUNCTIONS
复制标题
非循环抛物线夹头 Julia 组的孔隙率{ECKMANN 有理函数
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
M. Urba
中科院分区：
文献类型：
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作者：
F. Przytycki;M. Urba
证明了黎曼球面上的有理函数的Julia集是多孔的，其临界点包含在Julia集中的非回归点（但允许抛物周期点）。其次，引入了新的有理函数类：抛物Collet{Eckmann}和拓扑抛物Collet{Eckmann}，并证明了这两类函数的Julia集的平均多孔性。这意味着Julia集的上盒维数小于2。
It is proved that the Julia set of a rational function on the Riemann sphere whose critical points contained in the Julia set are non-recurrent (but parabolic periodic points are allowed) is porous. Next, new classes of rational functions: parabolic Collet{Eckmann and topological parabolic Collet{Eckmann are introduced and mean porosity of Julia sets for functions in these classes is proved. This implies that the upper box-counting dimension of the Julia set is less than 2 .