Tangent-Free Property for Periodic Cells Generated by Some General Piecewise Isometries

Figure 1

(a) The illustration to the invariant disks packing of the Sigma-Delta map for the parameter 𝜃=1.75. (b) The local magnification of the square [0,0.5]×[−0.25,0.25], we can see that the disk packing is very “loose” and there is no tangencies between any pair of invariant disks.

(a)

(b)