Dynamics of the p -adic Shift and Applications
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 coeffici...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Institute of Mathematical Sciences
2012
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| Online Access: | http://hdl.handle.net/1721.1/71153 |
| _version_ | 1826205227612635136 |
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| author | Kingsbery, James Levin, Alexander Preygel, Anatoly Silva, Cesar E. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kingsbery, James Levin, Alexander Preygel, Anatoly Silva, Cesar E. |
| author_sort | Kingsbery, James |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:09:22Z |
| format | Article |
| id | mit-1721.1/71153 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:09:22Z |
| publishDate | 2012 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | mit-1721.1/711532022-10-01T13:23:02Z Dynamics of the p -adic Shift and Applications Kingsbery, James Levin, Alexander Preygel, Anatoly Silva, Cesar E. Massachusetts Institute of Technology. Department of Mathematics Preygel, Anatoly Preygel, Anatoly Levin, Alexander 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. Williams College (Bronfman Science Center) National Science Foundation (U.S.) (REU Grant DMS – 0353634) 2012-06-14T18:51:01Z 2012-06-14T18:51:01Z 2011-02 2010-07 Article http://purl.org/eprint/type/JournalArticle 1553-5231 1078-0947 http://hdl.handle.net/1721.1/71153 Kingsbery, James et al. “Dynamics of the p -adic Shift and Applications.” Discrete and Continuous Dynamical Systems 30.1 (2011): 209–218. Web. en_US http://dx.doi.org/10.3934/dcds.2011.30.209 Discrete and Continuous Dynamical Systems - Series A 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. application/pdf American Institute of Mathematical Sciences AIMS |
| spellingShingle | Kingsbery, James Levin, Alexander Preygel, Anatoly Silva, Cesar E. Dynamics of the p -adic Shift and Applications |
| title | Dynamics of the p -adic Shift and Applications |
| title_full | Dynamics of the p -adic Shift and Applications |
| title_fullStr | Dynamics of the p -adic Shift and Applications |
| title_full_unstemmed | Dynamics of the p -adic Shift and Applications |
| title_short | Dynamics of the p -adic Shift and Applications |
| title_sort | dynamics of the p adic shift and applications |
| url | http://hdl.handle.net/1721.1/71153 |
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