Subdivision rules and virtual endomorphisms
- First Online:
- 37 Downloads
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.
KeywordsFinite subdivision rule Thurston map Virtual endomorphism
Mathematics Subject Classification (2000)37F10 52C20 20E08
Unable to display preview. Download preview PDF.