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Subdivision rules and virtual endomorphisms

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Abstract

Suppose f : S 2 → S 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.

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Authors and Affiliations

  1. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA

    J. W. Cannon

  2. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    W. J. Floyd

  3. Department of Mathematics, Eastern Michigan University, Ypsilanti, MI, 48197, USA

    W. R. Parry

  4. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA

    K. M. Pilgrim

Authors
  1. J. W. Cannon
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  2. W. J. Floyd
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  3. W. R. Parry
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  4. K. M. Pilgrim
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Correspondence to K. M. Pilgrim.

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Cannon, J.W., Floyd, W.J., Parry, W.R. et al. Subdivision rules and virtual endomorphisms. Geom Dedicata 141, 181–195 (2009). https://doi.org/10.1007/s10711-009-9352-7

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  • DOI: https://doi.org/10.1007/s10711-009-9352-7

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