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Luka Boc Thaler: Automorphisms of C^2 with non-recurrent Siegel cylinders

Date of publication: 19. 10. 2019
Complex analysis seminar
Torek, 22.10.2019 ob 12:30, soba 3.06 na Jadranski 21
V torek, 22. oktobra ob 12. uri in 30 minut, bo v okviru seminarja za kompleksno analizo predavanje

Luka Boc Thaler: Automorphisms of C^2 with non-recurrent Siegel cylinders.

Abstract: A non-recurrent Siegel cylinder is an invariant, non-recurrent Fatou component U of an automorphism F of C^2 satisfying:
(1) The closure of the omega-limit set of F on U contains an isolated fixed point,
(2) there exists a univalent map G from U  into C^2 conjugating F to the translation (z,w)-> (z+1,w), and
(3) every limit map of {F^n} on U  has one-dimensional image.
We prove the existence of non-recurrent Siegel cylinders. In fact, we provide an explicit class of maps having such Fatou components, and show that examples in this class can be constructed as compositions of shears and overshears. This is joint work with F. Bracci and H. Peters.

Seminar bo v predavalnici 3.06 na Jadranski 21. Vljudno vabljeni!

Vodji seminarja

Franc Forstnerič in Barbara Drinovec Drnovšek