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Subdivision rules and virtual endomorphisms |
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| Authors: | J. W. Cannon W. J. Floyd W. R. Parry K. M. Pilgrim |
| Affiliation: | (1) Department of Mathematics, Brigham Young University, Provo, UT 84602, USA;(2) Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA;(3) Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA;(4) Department of Mathematics, Indiana University, Bloomington, IN 47405, USA |
| 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. |
| Keywords: | Finite subdivision rule Thurston map Virtual endomorphism |
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