Theses and Dissertations - UTB/UTPA
Date of Award
Master of Science (MS)
Dr. Mrinal Kanti Roychowdhury
Dr. Timothy Huber
Dr. Virgil Pierce
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 µh 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 µh, 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.
University of Texas-Pan American
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