Geometriae Dedicata

, Volume 141, Issue 1, pp 181–195

Subdivision rules and virtual endomorphisms

  • J. W. Cannon
  • W. J. Floyd
  • W. R. Parry
  • K. M. Pilgrim
Original Paper

DOI: 10.1007/s10711-009-9352-7

Cite this article as:
Cannon, J.W., Floyd, W.J., Parry, W.R. et al. Geom Dedicata (2009) 141: 181. doi:10.1007/s10711-009-9352-7


Suppose f : S2S2 is a postcritically finite branched covering without periodic branch points. If f is the subdivision map of a finite subdivision rule with mesh going to zero combinatorially, then the virtual endomorphism on the orbifold fundamental group associated to f is contracting. This is a first step in a program to clarify the relationships among various notions of expansion for noninvertible dynamical systems with branching behavior.


Finite subdivision ruleThurston mapVirtual endomorphism

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • J. W. Cannon
    • 1
  • W. J. Floyd
    • 2
  • W. R. Parry
    • 3
  • K. M. Pilgrim
    • 4
  1. 1.Department of MathematicsBrigham Young UniversityProvoUSA
  2. 2.Department of MathematicsVirginia TechBlacksburgUSA
  3. 3.Department of MathematicsEastern Michigan UniversityYpsilantiUSA
  4. 4.Department of MathematicsIndiana UniversityBloomingtonUSA