On measure-preserving $\mathcal {C}^1$ transformations of compact-open subsets of non-archimedean local fields
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- by James Kingsbery, Alex Levin, Anatoly Preygel and Cesar E. Silva PDF
- Trans. Amer. Math. Soc. 361 (2009), 61-85 Request permission
Abstract:
We introduce the notion of a locally scaling transformation defined on a compact-open subset of a non-archimedean local field. We show that this class encompasses the Haar measure-preserving transformations defined by $\mathcal {C}^1$ (in particular, polynomial) maps, and prove a structure theorem for locally scaling transformations. We use the theory of polynomial approximation on compact-open subsets of non-archimedean local fields to demonstrate the existence of ergodic Markov, and mixing Markov transformations defined by such polynomial maps. We also give simple sufficient conditions on the Mahler expansion of a continuous map $\mathbb {Z}_p \to \mathbb {Z}_p$ for it to define a Bernoulli transformation.References
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Additional Information
- James Kingsbery
- Affiliation: Department of Mathematics, Williams College, Williamstown, Massachusetts 01267
- Email: 06jck@williams.edu
- Alex Levin
- Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
- Address at time of publication: Department of Mathematics, MIT, Cambridge, Massachusetts 02139
- Email: alex.levin@post.harvard.edu, levin@mit.edu
- Anatoly Preygel
- Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
- Address at time of publication: Department of Mathematics, MIT, Cambridge, Massachusetts 02139
- MR Author ID: 842366
- Email: preygel@post.harvard.edu, preygel@mit.edu
- Cesar E. Silva
- Affiliation: Department of Mathematics, Williams College, Williamstown, Massachusetts 01267
- MR Author ID: 251612
- Email: csilva@williams.edu
- Received by editor(s): September 1, 2006
- Published electronically: August 12, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 61-85
- MSC (2000): Primary 37A05; Secondary 37F10
- DOI: https://doi.org/10.1090/S0002-9947-08-04686-2
- MathSciNet review: 2439398