Subdivision rules and virtual endomorphisms
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- Cannon, J.W., Floyd, W.J., Parry, W.R. et al. Geom Dedicata (2009) 141: 181. doi:10.1007/s10711-009-9352-7
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Suppose f : S2 → S2 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.