论文标题
关于“卫星”的不变度量
On invariant measures of "satellite" infinitely renormalizable quadratic polynomials
论文作者
论文摘要
令F（z）= z^2+c为无限的可恢复性二次多项式，而j_ \ infty是其简单重新夸张的“小”朱莉娅集合的前轨道的相交。我们证明，如果F允许卫星重量化的无限序列，则在后临界集中支持f：j_ \ infty \ to j_ \ infty的每种不变量度，并具有零lyapunov指数。加上[G. Levin，F。Przytycki，W。Shen，《霍普诺夫图》的指数。发明。数学。 205（2016），363-382]，这意味着C在C处的Lyapunov指数等于零，这部分回答了Weixiao Shen提出的问题。
Let f(z)=z^2+c be an infinitely renormalizable quadratic polynomial and J_\infty be the intersection of forward orbits of "small" Julia sets of its simple renormalizations. We prove that if f admits an infinite sequence of satellite renormalizations, then every invariant measure of f: J_\infty\to J_\infty is supported on the postcritical set and has zero Lyapunov exponent. Coupled with [G. Levin, F. Przytycki, W. Shen, The Lyapunov exponent of holomorphic maps. Invent. Math. 205 (2016), 363-382], this implies that the Lyapunov exponent of such f at c is equal to zero, which answers partly a question posed by Weixiao Shen.
