Core Entropy of Finite Subdivision Rules

The topological entropy of the subdivision map of a finite subdivision rule restricted to the 1-skeleton of its model subdivision complex, which we call textbf{core entropy}, is examined. We consider core entropy for finite subdivision rules realizing quadratic Misiurewicz polynomials and matings of such polynomials. It is shown that for a non-restrictive class of finite subdivision rules realizing quadratic Misiurewicz polynomials, core entropy equals Thurston's core entropy. We also show that the core entropy of formal and degenerate matings of Misiurewicz polynomials is determined by Thurston's core entropy of the mated polynomials.