2023/08/29 by Alexander Blokh, Blokh, Alexander, Lex Oversteegen +3
Mathematics · #37C25 #37F10 #37F20 (Primary) #37F50 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2308.15580
openalex publication_date 2023/08/29 · openalex created_date 2023/09/02 · 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) QL 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.