2012/03/13 by Roychowdhury, Mrinal Kanti
#28A78 #28A80 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1203.2724
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.