论文标题
通过吸引和弱排斥固定点产生的间歇性
Intermittency generated by attracting and weakly repelling fixed points
论文作者
论文摘要
最近，对于一类批判性间歇性随机系统，发现了一个相变，以实现绝对连续不变的度量的有限。该结果所保留的系统的特征是在超大级吸引固定点和指数排除的固定点之间的相互作用。在本文中，我们考虑了一个紧密相关的随机系统家族，而是从两个固定点呈指数迅速吸引和多个快速的排斥，并表明这种相变仍然存在。但是，证明的方法是不同的，并且依赖于为转移操作员建造合适的不变设置。
Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay between a superexponentially attracting fixed point and an exponentially repelling fixed point. In this article we consider a closely related family of random systems with instead exponentially fast attraction to and polynomially fast repulsion from two fixed points, and show that such a phase transition still exists. The method of the proof however is different and relies on the construction of a suitable invariant set for the transfer operator.
