2023/12/29 by Gomes, Elena
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2312.17447
Let f be a polynomial-like mapping of the sphere of degree d ≥ 2. We show that the Julia set J(f) of f cannot be the union of a finite number of proper indecomposable subcontinua. As a corollary, we prove that J(f) is an indecomposable continuum if and only if there exists a prime end of some complementary region of J(f) whose impression is the entire J(f), generalizing a result by Childers, Mayer and Rogers.