Dia: Dimecres 29 d'abril de 2026
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Xavier Buff, Institut de Mathématiques de Toulouse
Títol: Spiralling domains for germs tangent to the identity (joint work with Jasmin Raissy)
Resum: We prove that if a is a non zero real parameter, the polynomial F:C^2 → C^2 defined by F(x,y) = (x + y^2 + ax(x-y),y+x^2+ay(x-y)) has infinitely many Fatou components in which orbits converge to the origin. We also prove that the projection of those orbits to CP^1 spiral along geodesics of a meromorphic affine structure. This study relates to the study of the real-time trajectories of a homogeneous vector field on C^2, to the study of an affine structure obtained by gluing the sides of a polygon via complex affine maps, and to the study of the Fuchsian group generated by the order three map z→1/(1-z) and by the translation z→z+T where T is a real number greater than 3.
Last updated: Fri Apr 24 16:12:39 2026