Dynamical systems workgroup

Asymptotic equidistribution of the solutions of the equation $R^n(\zeta)=z.$

Vanessa Matus de la Parra

Friday, February 7th, 2020
4:00 PM - 5:00 PM
Hylan1106A

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 $n$ goes to infinity.

Brolin’s result on asymptotic equidistribution of solutions of the equation $P^n(\zeta)=z$ for $P(z)\in\mathbb{C}[z]$ using potential theory has been really useful to inspire a lot of proofs of equidistribution of more general dynamical systems, as rational maps $R$ on the Riemann sphere (Ljubich, Freire-Lópes-Mañé), holomorphic maps on $\mathbb{P}^2$ (Friend-Duval), rational maps over a complete algebraically closed non-archimedian field (Favre - Rivera-Letelier, Baker-Rumely, Chambert-Loir), polynomial correspondences with Lojasiewicz exponent $\ell>1$ (Dinh), and so on.

We will continue to show the case of Rational maps on the Riemann Sphere.

Event contact: vmatusde at ur dot rochester dot edu