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Expansion properties for finite subdivision rules I

Authors
  • Floyd, William J.1
  • Parry, Walter R.2
  • Pilgrim, Kevin M.3
  • 1 Virginia Tech, Department of Mathematics, Blacksburg, VA, 24061, USA , Blacksburg (United States)
  • 2 Eastern Michigan University, Department of Mathematics and Statistics, Ypsilanti, MI, 48197, USA , Ypsilanti (United States)
  • 3 Indiana University, Department of Mathematics, Bloomington, IN, 47405, USA , Bloomington (United States)
Type
Published Article
Journal
Science China Mathematics
Publisher
Science China Press
Publication Date
Nov 22, 2018
Volume
61
Issue
12
Pages
2237–2266
Identifiers
DOI: 10.1007/s11425-016-9265-y
Source
Springer Nature
Keywords
License
Yellow

Abstract

Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate relationships between various notions of expansion—combinatorial, dynamical, algebraic, and coarse-geometric.

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