Toward the ergodicity of p-adic 1-Lipschitz functions represented by the van der Put series☆
Toward the ergodicity of p-adic 1-Lipschitz functions represented by the van der Put series☆
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DOI：
10.1016/j.jnt.2013.02.006
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发表时间：
2012-10
影响因子：
0.7
通讯作者：
Sangtae Jeong
中科院分区：
文献类型：
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作者：
Sangtae Jeong
Yurova (2010) [17] 和 Anashin 等人。 (2011 [3]，预印本 [4]) 根据 van der Put 展开式描述 Z2 上 1-Lipschitz 函数的遍历性。受他们最近工作的启发，我们为在更一般的设置 Zp 上定义的函数的遍历性提供了充分的条件。此外，我们还为 Z2 上的遍历 1-Lipschitz 函数提供了两个标准的替代证明（由于 Anashin 等人，2011 [3]，预印本 [4] 和 Yurova，2010 [17]），由 Mahler 基和 van der Put 基表示。
Yurova (2010) [17] and Anashin et al. (2011 [3], preprint [4]) characterize the ergodicity of a 1-Lipschitz function on Z2in terms of the van der Put expansion. Motivated by their recent work, we provide the sufficient conditions for the ergodicity of such a function defined on a more general setting Zp. In addition, we provide alternative proofs of two criteria (because of Anashin et al., 2011 [3], preprint [4] and Yurova, 2010 [17]) for an ergodic 1-Lipschitz function on Z2, represented by both the Mahler basis and the van der Put basis.