From the clique polynomial to the core entropy

The core entropy of quadratic polynomials, recently introduced by W. Thurston,
is a dynamical invariant which can be defined purely in combinatorial terms, and
provides a useful tool to study parameter spaces of polynomials.

A classical tool to compute the entropy of a dynamical system is the clique polynomial
(recently used by McMullen to study the entropy of pseudo-Anosov maps).
We will develop an infinite version of the clique polynomial for infinite graphs,
and use it to study the symbolic dynamics of Hubbard trees.

Using these methods we will prove that the core entropy of quadratic polynomials
varies continuously as a function of the external angle, answering a question of Thurston.