Dynamics of the p -adic Shift and Applications
Name
Levin-2011-Dynamics of the p-adic.pdf
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181.52 KB
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Checksum (MD5)
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Author(s)
Kingsbery, James
Levin, Alexander
Preygel, Anatoly
Silva, Cesar E.
Date Issued
February 2011
Journal
Discrete and Continuous Dynamical Systems - Series A
Publisher
American Institute of Mathematical Sciences
Citation
Kingsbery, James et al. “Dynamics of the p -adic Shift and Applications.” Discrete and Continuous Dynamical Systems 30.1 (2011): 209–218. Web.
Version
Final published version
Abstract
There is a natural continuous realization of the one-sided Bernoulli shift on the [p] -adic integers as the map that shifts the coefficients of the [p] -adic expansion to the left. We study this map's Mahler power series expansion. We prove strong results on [p] -adic valuations of the coefficients in this expansion, and show that certain natural maps (including many polynomials) are in a sense small perturbations of the shift. As a result, these polynomials share the shift map's important dynamical properties. This provides a novel approach to an earlier result of the authors.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3934/dcds.2011.30.209
