|Date: Monday, October 30, 2017
Location: 3096 East Hall (4:00 PM to 5:00 PM)
Title: Iterated Elliptic Functions: Dynamics and Parametrizations
Abstract: The Weierstrass P function is the classical doubly periodic meromorphic function of a complex variable; iterating it gives surprisingly diverse dynamics. We show that the dynamics of the function P depend on the lattice of periodicity, and within each lattice shape (e.g., square), the dynamics vary greatly by changing lattice generators. We discuss properties of Julia and Fatou sets in this setting, along with maps of the form P+b, where b is a complex constant. Less surprising is that the addition of the constant adds even more dynamical diversity for each fixed lattice. The tools rely on some beautiful classical identities for elliptic functions; we also mention some results about ergodic measures for elliptic functions.
Speaker: Jane Hawkins
Institution: UNC Chapel Hill