Subdivision rules and virtual endomorphisms
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.
KeywordsFinite subdivision rule Thurston map Virtual endomorphism
Mathematics Subject Classification (2000)37F10 52C20 20E08
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