, Volume 141, Issue 1, pp 181-195
Date: 25 Jan 2009

Subdivision rules and virtual endomorphisms

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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.