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Science China Mathematics

, Volume 61, Issue 12, pp 2237–2266 | Cite as

Expansion properties for finite subdivision rules I

  • William J. Floyd
  • Walter R. Parry
  • Kevin M. Pilgrim
Articles
  • 14 Downloads

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.

Keywords

finite subdivision rule expanding map postcritically finite Thurston map 

MSC(2010)

37F10 52C20 57M12 

Notes

Acknowledgements

Kevin M. Pilgrim was supported by Simons Foundation Collaboration Grants for Mathematicians (Grant No. 245269). The authors express heartfelt gratitude to Jim Cannon, who helped them in many ways. Without him this paper would not exist.

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Copyright information

© Science in China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • William J. Floyd
    • 1
  • Walter R. Parry
    • 2
  • Kevin M. Pilgrim
    • 3
  1. 1.Department of MathematicsVirginia TechBlacksburgUSA
  2. 2.Department of Mathematics and StatisticsEastern Michigan UniversityYpsilantiUSA
  3. 3.Department of MathematicsIndiana UniversityBloomingtonUSA

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