On ergodicity of p-adic dynamical systems for arbitrary prime p
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In this paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of 1-Lipschitz p-adic functions that are defined on (and valuated in) the space ℤ p of p-adic integers for any prime p. The conditions are stated in terms of coordinate representations of p-adic functions.
Key wordsergodicity 1-Lipschitz p-adic functions p-adic numbers
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- 4.V. Anashin, “Ergodic transformations in the space of p-adic integers,” Proc. of 2nd Int. Conf. on p-Adic Mathematical Physics (Belgrade, Serbia and Montenegro, 15–21 Sep., 2005), AIP Conf. Proc. 826, 3–24 (AIP, Melville, New York, 2006).Google Scholar