Abstract
Let M 2 M_2 be the space of quadratic rational maps f : P 1 → P 1 f:\textbf {P}^1\to \textbf {P}^1 , modulo the action by conjugation of the group of Möbius transformations. In this paper a compactification X X of M 2 M_2 is defined, as a modification of Milnor’s M ¯ 2 ≃ CP 2 \overline {M}_2\simeq \textbf {CP}^2 , by choosing representatives of a conjugacy class [ f ] ∈ M 2 [f]\in M_2 such that the measure of maximal entropy of f f has conformal barycenter at the origin in R 3 \textbf {R}^3 and taking the closure in the space of probability measures. It is shown that X X is the smallest compactification of M 2 M_2 such that all iterate maps [ f ] ↦ [ f n ] ∈ M 2 n [f]\mapsto [f^n]\in M_{2^n} extend continuously to X → M ¯ 2 n X \to \overline {M}_{2^n} , where M ¯ d \overline {M}_d is the natural compactification of M d M_d coming from geometric invariant theory.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
