  As defined by W. Thurston, the core entropy of a polynomial is the entropy of
the restriction to its Hubbard tree. For each d >= 2, we study the core entropy
as a function on the parameter space of polynomials of degree d, and prove it
varies continuously both as a function of the combinatorial data and of the
coefficients of the polynomials. This generalizes a conjecture of Thurston for
quadratic polynomials.
