(a) Find the box-counting dimension of the invariant set of the skinny baker map.

(b) Describe 3-dimensional versions of the attractors in Figures 4.3, 4.4, and 4.5

(c) Compute the dimension of these versions from pt (b).

THANK YOU

1/2 0 1/3 2/3 1 0 113 213 1 0 113 213 1 Figure 4.3 Definition of the skinny baker map. (a) The top half maps to the right strip. The bottom half maps to the left strip. (b) The second and (c) third iterate of the map. In the limit, the invariant set is a Cantor middle-third set of vertical lines. 1/2 0 1/3 2/3 1 0 113 213 1 0 113 213 1 Figure 4.3 Definition of the skinny baker map. (a) The top half maps to the right strip. The bottom half maps to the left strip. (b) The second and (c) third iterate of the map. In the limit, the invariant set is a Cantor middle-third set of vertical lines