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Joanna Furno

University of Houston



Measuring Julia sets in finite extensions of the \(p\)-adic numbers



September 11, 2017
1:00 pm    PHG 646



Abstract
 

Haar measure and Hausdorff dimension are two possible methods of measuring size in the field of \(p\)-adic numbers and its finite extensions. We first explore the Haar measure and Hausdorff dimension for balls in a finite extension of the \(p\)-adic number. Then we use these two tools to measure the size of the Julia set for some \(p\)-adic repellers. Finally, we give some concrete polynomial examples from among these \(p\)-adic repellers.






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