1997/09/15 by John H. Hubbard, Hubbard, John, Peter Papadopol +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.math/9709227
openalex publication_date 1997/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In \cite HO1, it was shown that there is a topology on \C2\sqcup S3 homeomorphic to a 4-ball such that the Hénon mapping extends continuously. That paper used a delicate analysis of some asymptotic expansions, for instance, to understand the structure of forward images of lines near infinity. The computations were quite difficult, and it is not clear how to generalize them to other rational maps. In this paper we will present an alternative approach, involving blow-ups rather than asymptotics. We apply it here only to Hénon mappings and their compositions, but the method should work quite generally, and help to understand the dynamics of rational maps f:\Proj2\ratto\Proj2 with points of indeterminacy. The application to compositions of Hénon maps proves a result suggested by Milnor, involving embeddings of solenoids in S3 which are topologically different from those obtained from Hénon mappings.