School of Mathematics and Natural Sciences

Seminar: Josias Reppekus (G.15.25)

27.10.2022|14:15 Uhr

Identifying Fatou components with PSH functions

I would like to invite you for coming Thursday, 27.10.2022 at 16:15 in room G.15.25 at Wuppertal University to attend my talk:

-- Identifying Fatou components with PSH functions --

I want to present a technique of identifying Fatou components of holomorphic maps using properties of plurisubharmonic functions with some examples of successful applications and some examples where one could hope to apply similar methods.

A Fatou component of a holomorphic self-map F of a complex manifold is a maximal connected open set of stable dynamics.

The hardest part in identifying a Fatou component is often proving maximality.

In 2019, Arosio, Benini, Fornaess, Peters identified a candidate component with dynamics tending to infinity by constructing a plurisubharmonic function encoding the dynamics of F on a hypothetical bigger containing component and reaching a contradiction by finding an open set inside of a polar set.

I will present their example and two examples with convergence to a finite point where I expect a similar argument should work, if one can find the correct plurisubharmonic function.

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