| In this thesis, first we have defined the topological pressure P(t) and then using Banach limit we have determined a unique Borel probability measure microh supported by the invariant set E of a system of bi-Lipschitz mappings where h is the unique zero of the pressure function. Using the topological pressure and the measure microh, under certain condition on bi-Lipschitz constants, we have shown that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension of the set E are all equal to h. Moreover, it is shown that the h-dimensional Hausdorff measure and the h-dimensional packing measure are finite and positive. |
