Dynamical systems workgroup

Asymptotic equidistribution of solutions of the equation

Vanessa Matus de la Parra

Friday, January 24th, 2020
3:00 PM - 6:00 PM
Hylan 1106A

We say that a sequence of finite sets indexed by $n$ is asymptotically equidistributed if the sequence of uniform measures (average of Dirac masses in each point of the set) converges to a limit measure when goes to infinity.

Brolin’s result on asymptotic equidistribution of solutions of the equation for using potential theory has been really useful to inspire a lot of proofs of equidistribution of more general dynamical systems, as rational maps on the Riemann sphere (Ljubich, Freire-Lópes-Mañé), holomorphic maps on (Friend-Duval), rational maps over a complete algebraically closed non-archimedian field (Favre - Rivera-Letelier, Baker-Rumely, Chambert-Loir), polynomial correspondences with Lojasiewicz exponent (Dinh), and so on.

We will show how to use potential theory in the case of Brolin’s result as an starting point on the use of this important tool.

Event contact: vmatusde at ur dot rochester dot edu