Measure-preservation criteria for a certain class of 1-lipschitz functions on Zp in mahler's expansion

Sangtae Jeong; Chunlan Li

doi:10.3934/dcds.2017160

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2017, Volume 37, Issue 7: 3787-3804. Doi: 10.3934/dcds.2017160

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Measure-preservation criteria for a certain class of 1-lipschitz functions on Z_p in mahler's expansion

Sangtae Jeong^, and
Chunlan Li

Department of Mathematics, Inha University, Incheon, 22212, Korea

^* Corresponding author
^* Corresponding author

Received: July 31, 2016

Revised: January 31, 2017

Published: August 2017

The first author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2016R1D1A1B03930281)

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Abstract

In this paper, we formulate a conjecture for a measure-preservation criterion of 1-Lipschitz functions defined on the ring Z_p of p-adic integers, in terms of Mahler's expansion. We then provide evidence for this conjecture in the case that p = 3, and verify that it also holds for a wider class of 1-Lipschitz functions that are everywhere differentiable on Z_p, which we call $\mathcal{ B}$-functions, in the sense of Anashin.

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Mathematics Subject Classification: 37P20 (11S80, 11S82, 37A45).

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