Polynomial Basins of Infinity

Laura DeMarco*, Kevin M. Pilgrim

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study the projection π: Md→Bdwhich sends an affine conjugacy class of polynomial f: ℂ→ℂto the holomorphic conjugacy class of the restriction of f to its basin of infinity. When Bdis equipped with a dynamically natural Gromov-Hausdorff topology, the map π becomes continuous and a homeomorphism on the shift locus. Our main result is that all fibers of π are connected. Consequently, quasiconformal and topological basin-of-infinity conjugacy classes are also connected. The key ingredient in the proof is an analysis of model surfaces and model maps, branched covers between translation surfaces which model the local behavior of a polynomial.

Original languageEnglish (US)
Pages (from-to)920-950
Number of pages31
JournalGeometric and Functional Analysis
Volume21
Issue number4
DOIs
StatePublished - Aug 1 2011

Keywords

  • Fatou set
  • basin of infinity
  • moduli space
  • polynomial

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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