2013/10/10 by Fei Yang, Yang, Fei
Mathematics · Physics and Astronomy · #37F30 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 37F45 #Quantum chaos and dynamical systems #Secondary 37F10
paper · pdf · doi:10.48550/arxiv.1310.2802
openalex publication_date 2013/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f be a rational map with degree at least two. We prove that f has at least 2 disjoint and infinite critical orbits in the Julia set if it has a Herman ring. This result is sharp in the following sense: there exists a cubic rational map having exactly two critical grand orbits but also having a Herman ring. In particular, f has no Herman rings if it has at most one infinite critical orbit in the Julia set. These criterions derive some known results about the rational maps without Herman rings.