Dynamics
Description: The Thurston Set is a subset of the complex plane. The structure of this set encodes information about a particular family of dynamical systems -- specifically, about the entropies of polynomials of degree 2 whose critical points are periodic. The entropy of a dynamical system is a number that measures how "chaotic" the system is. It turns out that for dynamical systems in this family, e^entropy can only be a special kind of number (called a weak Perron number) -- but it is still a mystery which of these numbers can be represented this way. Any number that does arise in this way must be the solution to a polynomial with integer coefficients, so we can also look at the other roots of these polynomials (called Galois conjugates). The Thurston set is obtained by plotting all roots of all the polynomials associated to all the e^entropies of polynomials in this family. Studying the Thurston set is a way of investigating the question "which numbers arise as entropies of polynomials in this family?"