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Giovedì 16 dicembre ore 14, seminario dr. Josias Reppekus "Non-trivial limit sets of Fatou components"

Giovedì 16 dicembre 2021 alle ore 14:00 presso l'Aula F del Plesso di Matematica/Informatica il Dr. Josias Reppekus della University of Wuppertal, terrà un seminario dal titolo: 

"Non-trivial limit sets of Fatou components".

Tutti gli interessati sono invitati a partecipare. 

Organizzatrice: prof.ssa Anna Benini


A central object of interest when describing the dynamics of a holomorphic self-map F of a complex manifold is the Fatou set of points with stable dynamical behaviour and its connected components, called Fatou components. A Fatou component is invariant, if F maps it inside itself. In one variable, an invariant Fatou component either admits a conjugation of F to a rotation or all its orbits accumulate at a single fixed point of F. In other words, the limit set has either full dimension 1 or trivial dimension 0.

One of the many new phenomena in dimension 2 is that the orbits of an invariant Fatou component may accumulate on a limit set of intermediate dimension 1. In this talk, I will present classification results on Fatou components with limit sets of dimension 1 and construct examples not arising as straightforward products of one-dimensional components in the categories of endomorphisms of projective space and automorphisms of \mathbb{C}^2 .

Pubblicato Martedì, 7 Dicembre, 2021 - 17:49 | ultima modifica Martedì, 7 Dicembre, 2021 - 17:56