Non-ergodic maps in the tangent family

被引：9
|
作者：
Skorulski, B [1 ]
机构：
[1] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00661 Warsaw, Poland
来源：
INDAGATIONES MATHEMATICAE-NEW SERIES | 2003年 / 14卷 / 01期
关键词：
D O I：
10.1016/S0019-3577(03)90074-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider maps in the tangent family for which the asymptotic values are eventually mapped onto poles. For such functions the Julia set J(f) = (C) over bar. We prove that for almost all z is an element of J(f) the limit set W(z) is the post-singular set and f is non-ergodic on J(f). We also prove that for such f does not exist a f-invariant measure absolutely continuous with respect to the Lebesgue measure finite on compact subsets of C.
引用
收藏
页码：103 / 118
页数：16
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