p-Adic dynamics and angle doubling |
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Authors: | M. Maller J. Whitehead |
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Affiliation: | 1. Mathematics Department, Queens College, CUNY, Flushing, NY, 11367, USA 2. Computer Science Department, Queens College, CUNY, Flushing, NY, 11367, USA
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Abstract: | We consider the squaring map over the p-adic numbers for an odd prime p, and study its symbolic dynamics on the unit circle in ? p , the p-adic integers. When the map is restricted to the set of squares, we show an equivalence to angle doubling (mod 1) for rational angles. For primes p ≡ 3 (mod 4), this map may be represented as a unitary permutation matrix of the type used in quantum phase estimation. |
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