一类拟正则正弦映射的混沌动力学
Chaotic dynamics of a quasiregular sine mapping
摘要：
本文研究拟正则映射S：\R^d \to \R^d的迭代行为，它是一个正弦函数的模拟.证明了S的周期点构成\R^d的稠密子集.我们还证明了这个映射的朱利亚集是\R^d，在这个意义下，任何非空开集在S下的前向轨道是整个空间\R^d . Bergweiler和Eremenko证明了逃逸集I（S）在\R^d中也是稠密的。
英文摘要：
This article studies the iterative behaviour of a quasiregular mapping S:\R^d\to\R^d that is an analogue of a sine function. We prove that the periodic points of S form a dense subset of \R^d. We also show that the Julia set of this map is \R^d in the sense that the forward orbit under S of any non-empty open set is the whole space \R^d. The map S was constructed by Bergweiler and Eremenko who proved that the escaping set I(S) is also dense in \R^d.
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