2021/02/20 by Alexander Blokh, Blokh, Alexander, Lex Oversteegen +3
Mathematics · #37F10 #37F50 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Meromorphic and Entire Functions #Primary 37F20 #Secondary 37C25
paper · pdf · doi:10.48550/arxiv.2102.10325
openalex publication_date 2021/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 b∈ 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.