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<p>We provide a complete description of the dynamics of isometric uniformly differentiable functions on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {Z}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> using some new representations of the isometric transformations including permutations on the set <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\{0, 1\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>. We obtain some ergodicity criteria on compact subsets of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {Z}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> by proving the transitivity of finite orders.</p>

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Dynamics of Measure-Preserving Uniformly Differentiable Functions on the Ring of 2-Adic Integers

  • 期刊论文

  • 发表日期：

    2026年3月26日

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  • Nacima Memić,
  • Amil Pečenković

摘要

We provide a complete description of the dynamics of isometric uniformly differentiable functions on \(\mathbb {Z}_{2}\) Z 2 using some new representations of the isometric transformations including permutations on the set \(\{0, 1\}\) { 0 , 1 } . We obtain some ergodicity criteria on compact subsets of \(\mathbb {Z}_{2}\) Z 2 by proving the transitivity of finite orders.