# American Institute of Mathematical Sciences

July  2017, 37(7): 3787-3804. doi: 10.3934/dcds.2017160

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

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

* Corresponding author

Received  August 2016 Revised  February 2017 Published  April 2017

Fund Project: 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)

In this paper, we formulate a conjecture for a measure-preservation criterion of 1-Lipschitz functions defined on the ring Zp 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 Zp, which we call $\mathcal{ B}$-functions, in the sense of Anashin.

Citation: Sangtae Jeong, Chunlan Li. Measure-preservation criteria for a certain class of 1-lipschitz functions on Zp in mahler's expansion. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3787-3804. doi: 10.3934/dcds.2017160
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