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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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.
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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