Special curves and postcritically finite polynomials

Matthew Baker, Laura Grace DeMarco

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

Abstract

We study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations, in two settings: (1) rational curves that are polynomially parameterized; and (2) cubic polynomials defined by a given fixed point multiplier. We offer a conjecture on the general form of algebraic subvarieties in the moduli space of rational maps on P1 containing a Zariski-dense subset of postcritically finite maps.

Original languageEnglish (US)
Article numbere2
JournalForum of Mathematics, Pi
Volume1
DOIs
StatePublished - Jan 1 2013

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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