2011/01/07 by Daniel A. Nicks, Nicks, Daniel A.
Mathematics · #30C62 #30C65 #37F50 (Primary) 37F10 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic and Geometric Analysis #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1101.1483
openalex publication_date 2011/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that wandering domains can exist in the Fatou set of a polynomial type quasiregular mapping of the plane. We also give an example of a quasiregular mapping of the plane, with an essential singularity at infinity, which has a sequence of wandering domains contained in a bounded part of the plane. This contrasts with the situation in the analytic case, where wandering domains are impossible for polynomials and, for transcendental entire functions, the existence of wandering domains in a bounded part of the plane has been an open problem for many years.