The cookie-cutter-like set is defined as the limit set of a sequence of classical cookie-cutter mappings. For this cookie-cutter set it is shown that the topological pressure function exists, and that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension are all equal to the unique zero h of the pressure function. Moreover, it is shown that the h-dimensional Hausdorff measure and the h-dimensional packing measure are finite and positive.
Roychowdhury MK. Topological Pressure and Fractal Dimensions of Cookie-Cutter-Like Sets. Southeast Asian Bulletin of Mathematics. 2020;44(5):719-732.
Southeast Asian Bulletin of Mathematics