Spiraling domains in dimension 2, Xavier Buff (Institut de Mathématiques de Toulouse, France)
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Monday, 25. April 2022, 15:00
- Abstract: I will present a work in progress with Jasmin Raissy. We are studying the complex dynamics of the map $(x,y) \rightarrow (x+y^2+2x^2y,y+x^2+2y^2x)$. This polynomial map fixes the origin in $C^2$ and is tangent to the identity at the origin. We are trying to prove that the interior of the basin of attraction of the origin contains infinitely many fixed connected components. Those fixed components are closely related to the periodic trajectories in an equilateral triangular billiard.