Geometriae Dedicata

, Volume 141, Issue 1, pp 181–195 | Cite as

Subdivision rules and virtual endomorphisms

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

Abstract

Suppose f : S 2S 2 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.

Keywords

Finite subdivision rule Thurston map Virtual endomorphism 

Mathematics Subject Classification (2000)

37F10 52C20 20E08 

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References

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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

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