Topological conditions for the existence of absorbing Cantor sets
Topological conditions for the existence of absorbing Cantor sets
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DOI：
10.1090/s0002-9947-98-02109-6
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发表时间：
1998
影响因子：
1.3
通讯作者：
H. Bruin
中科院分区：
文献类型：
--
作者：
H. Bruin
本文讨论了s -单峰函数f的奇异吸引子。它推广了先前的结果，给出了非常一般的拓扑条件，即i)保证在f的临界点充分简并时存在吸收康托集，或ii)完全禁止存在吸收康托集。作为一个副产品，我们得到了非常弱的拓扑条件，暗示了f的绝对连续不变概率测度的存在。
This paper deals with strange attractors of S-unimodal rnaps f. It generalizes earlier results in the sense that very general topological conditions are given that either i) guarantee the existence of an absorbing Cantor set provided t:he critical point of f is sufficiently degenerate, or ii) prohibit the existence of an absorbing Cantor set altogether. AS a by-product we obtain very weak topological conditions that imply the existence of an absolutely continuous invariant probability measure for f.