On the postcritical set of a rational map

Laura G. DeMarco*, Sarah C. Koch, Curtis T. McMullen

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

The postcritical set P(f) of a rational map f: P1→ P1 is the smallest forward invariant subset of P1 that contains the critical values of f. In this paper we show that every finite set X⊂ P1(Q¯) can be realized as the postcritical set of a rational map. We also show that every map F: X→ X defined on a finite set X⊂ P1(C) can be realized by a rational map f: P(f) → P(f) , provided we allow small perturbations of the set X. The proofs involve Belyi’s theorem and iteration on Teichmüller space.

Original languageEnglish (US)
JournalMathematische Annalen
Volume377
Issue number1-2
DOIs
StatePublished - Jun 1 2020

ASJC Scopus subject areas

  • Mathematics(all)

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