Wandering domains and commuting functions [ Back ]

Date:
27.10.14   
Times:
15:30 to 16:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Anna Benini
University:
Centro di Ricerca Matematica Ennio di Giorgi

Abstract:

In complex dynamics, the phase space splits into two completely invariant subsets, the Fatou set on which the dynamics is stable and the Julia on which the dynamics is chaotic. A full classification of Fatou components is known, and there is a type of Fatou components called wandering domains which only appears in the transcendental case. Two rational entire functions commute only if their Fatou and Julia sets are equal, while the proof of the same result for transcendenal entire functions is yet to day challenged by the presence of wandering domains. We will describe transcendental dynamics and the the state of the problem giving several examples.