Infinite friezes of affine type $D$

Résumé

Triangulations of a twice punctured disk with at least two marked points on the boundary are associated to cluster categories of affine type $D$. Indecomposable objects in these categories can be arranged in three tubes using the Auslander-Reiten quiver, and the evaluation of the corresponding cluster variables give infinite friezes. We study these three friezes and their corresponding arcs on the surface and show that their three growth coefficients are equal.