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Orbit equivalence of \(p\)-adic transformations and their iterates

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Abstract

Orbit equivalence is a weaker notion of equivalence than isomorphism for measurable systems. We examine \(p\)-adic transformations in various orbit equivalence classes, including an example that preserves an infinite measure. Although \(p\)-adic transformations have been studied with respect to Haar measure, we use other i.i.d. product measures to see examples of different orbit equivalence classes. Since translation by an integer is an iterate of translation by 1, we gain an understanding of the possible behaviors of orbit equivalence classes under iteration.

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Acknowledgments

The results in this paper are part of the author’s Ph.D. dissertation at the University of North Carolina at Chapel Hill [53]. The author would like to thank Jane Hawkins, her adviser, for her guidance and encouragement. The author would also like to thank the referees for their careful reading and helpful suggestions.

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  1. Department of Mathematics and Computer Science, Dickinson College, PO Box 1773, Carlisle, PA, 17013, USA

    Joanna Furno

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  1. Joanna Furno
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Correspondence to Joanna Furno.

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Communicated by H. Bruin.

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Furno, J. Orbit equivalence of \(p\)-adic transformations and their iterates. Monatsh Math 175, 249–276 (2014). https://doi.org/10.1007/s00605-014-0645-z

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  • DOI: https://doi.org/10.1007/s00605-014-0645-z

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