2004/12/21 by Laura DeMarco, DeMarco, Laura · 2 citations
Mathematics · #37F45 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.AG #math.DS #msc:37F45
paper · pdf · doi:10.48550/arxiv.math/0412438
38 pages, 3 figures
arxiv created 2004/12/21 · openalex publication_date 2004/12/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M2 be the space of quadratic rational maps f:\bf P1→\bf P1, modulo the action by conjugation of the group of Möbius transformations. In this paper a compactification X of M2 is defined, as a modification of Milnor's M2\iso\bf CP2, by choosing representatives of a conjugacy class [f]∈ M2 such that the measure of maximal entropy of f has conformal barycenter at the origin in \bf R3, and taking the closure in the space of probability measures. It is shown that X is the smallest compactification of M2 such that all iterate maps [f]↦ [fn]∈ M2n extend continuously to X → M2n, where Md is the natural compactification of Md coming from geometric invariant theory.