9 apr 2019 -- 16:00
Aula D'Antoni, Roma Tor Vergata
Seminario di Analisi Complessa, nell’ambito del progetto MATH@TOV
Abstract.
Let $K$ be a compact subset of the unit disk $\mathbb{D}$. We will examine the asymptotic behavior of its trajectory under a semigroup of holomorphic self-maps $(\phi_t)_{t \geq 0}$ of $\mathbb{D}$.
The compact set $\phi_t(K)$ shrinks to the Denjoy-Wolff point of the semigroup, as $t \to + \infty$.
But what happens to its size?
In order to observe the behavior of the size of $\phi_t(K)$, we will use several geometric and potential theoretic quantities, such as hyperbolic area, harmonic measure and Green equilibrium potential.