Measure-preservation criteria for a certain class of 1-lipschitz functions on Z<sub><i>p</i></sub> in mahler's expansion

作者：Sangtae Jeong, Chunlan Li · 发表于：Discrete and Continuous Dynamical Systems · 年份：2017 · DOI：10.3934/dcds.2017160 · 被引用次数：13 · 研究领域：advanced mathematical theories、Mathematical Dynamics and Fractals、Algebraic Geometry and Number Theory

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.