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

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