%0 Generic %1 blokh2021immediate %A Blokh, Alexander %A Oversteegen, Lex %A Timorin, Vladlen %D 2021 %K complex_dynamics polynomial_dynamics renormalization %T Immediate renormalization of complex polynomials %U http://arxiv.org/abs/2102.10325 %X A cubic polynomial $P$ with a non-repelling fixed point $b$ is said to be immediately renormalizable if there exists a (connected) quadratic-like invariant filled Julia set $K^*$ such that $bK^*$. 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.

@preprint{blokh2021immediate, abstract = {A cubic polynomial $P$ with a non-repelling fixed point $b$ is said to be \emph{immediately renormalizable} if there exists a (connected) quadratic-like 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.}, added-at = {2021-03-15T23:25:20.000+0100}, author = {Blokh, Alexander and Oversteegen, Lex and Timorin, Vladlen}, biburl = {https://www.bibsonomy.org/bibtex/2b51df2012765511de6c172a9893c4394/lukas.geyer}, description = {Immediate renormalization of complex polynomials}, interhash = {a46865e114a2c8af5931839af414bbe1}, intrahash = {b51df2012765511de6c172a9893c4394}, keywords = {complex_dynamics polynomial_dynamics renormalization}, note = {cite arxiv:2102.10325Comment: 34 pages, 2 figures}, timestamp = {2021-03-15T23:25:20.000+0100}, title = {Immediate renormalization of complex polynomials}, url = {http://arxiv.org/abs/2102.10325}, year = 2021 }