Lauwerier映射的奇怪吸引子的遍历性及其结构

本又考虑Ｌａｕｗｅｒｉｅｒ映射Ｆａ，ｂ（ｘ，ｙ）＝（ｂｘ（１－２ｙ）＋ｙ，ａｙ（１－ｙ））．我们证明对于参数α在一个正测度集合中，对应的映射有非平凡的拓扑可迁的吸引子，其中是某个双曲不动点的不稳定集的闭包．周期点是双曲的且在中稠密，而且中任两个周期点异宿相关（稳定与不稳定集的横截相交）．同时也构造支撑在吸引子上的Ｓｉｎａｌ－Ｂｏｗｅｎ－Ｒｕｅｌｌｅ测度，并研究其性质．

The Ergodic Properties and the Structure of Strange Attractor in Lauwerier Map

in this paper, the Lauwerier map Fa,b(x,y) = (bx(1 - 2y) y, ay(1 - 2y))is considered. We prove that for Parameter a in a set with positive measure, thecorresponding map possesses a nontrivial topologically trajnsitive attractor A, this A isthe closure of the unstable set of some fixed point. Periodic points are dense in A andall of them are hyperbolic. Moreover any two periodic points in A are heteroclinicajlyrelated (transversal intersection of stable and unstable sets). We also construct theSinal-Bowen-Ruelle measure supported on attrastor and study it properties.