Alexander Blokh, Lex Oversteegen, Vladlen Timorin
Published 2023-08-29Version 1
A cubic polynomial $P$ with a non-repelling fixed point $b$ is said to be immediately renormalizable if there exists a (connected) QL invariant filled Julia set $K^*$ such that $b\in K^*$. In that case, exactly one critical point of $P$ does not belong to $K^*$. We show that if, in addition, the Julia set of $P$ has no (pre)periodic cutpoints, then this critical point is recurrent.
Comments: 26 pages, 1 figure; accepted to a special issue of the MMJ dedicated to Yulij Ilyashenko's 80th Birthday. arXiv admin note: substantial text overlap with arXiv:2102.10325
Immediate renormalization of complex polynomials
Singular values and bounded Siegel disks
Equidistribution of critical points of the multipliers in the quadratic family
![QR code for arXiv:2308.15580 [math.DS]](http://oss.arxitics.com/images/favicon.svg)