Backward stability for polynomial maps with locally connected Julia sets
Backward stability for polynomial maps with locally connected Julia sets
复制标题
DOI：
10.1090/s0002-9947-03-03415-9
复制
发表时间：
2003-08
影响因子：
1.3
通讯作者：
A. Blokh;L. Oversteegen
中科院分区：
文献类型：
--
作者：
A. Blokh;L. Oversteegen
我们研究了具有弱扩展特性的非屏蔽平面连续体的拓扑动力学，并证明了不存在漂移连续体意味着后向稳定性。然后我们由此推断，具有局部连通 Julia 集的多项式 f 在其吸引环和中性环的任何邻域之外都是后向稳定的。对于共形测量 μ，这很容易意味着以下条件之一成立： 1. 对于 μ-a.e. x E J(f), ω(x) = J(f); 2. 对于 μ-a.e. x ∈ J(f), ω(x) = ω(c(x)) 对于取决于 x 的临界点 c(x)。
We study topological dynamics on unshielded planar continua with weak expanding properties at cycles for which we prove that the absence of wandering continua implies backward stability. Then we deduce from this that a polynomial f with a locally connected Julia set is backward stable outside any neighborhood of its attracting and neutral cycles. For a conformal measure μ this easily implies that one of the following holds: 1. for μ-a.e. x E J(f), ω(x) = J(f); 2. for μ-a.e. x ∈ J(f), ω(x) = ω(c(x)) for a critical point c(x) depending on x.