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<p>We study the conditional measures of every invariant probability measure for every <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^{1+\gamma }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>+</mo> <mi>γ</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> diffeomorphism of a closed Riemannian manifold, and we show that they always admit an asymptotic local product structure. This is a direct application of the notion of <i>tubular dimension</i> which we introduce and study in the manuscript. As an additional application we prove a bound on any two consecutive conditional entropies in terms of volume growth.</p>

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Tubular Dimension: Leaf-Wise Asymptotic Local Product Structure, and Entropy and Volume Growth

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月20日

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  • Snir Ben Ovadia

摘要

We study the conditional measures of every invariant probability measure for every \(C^{1+\gamma }\) C 1 + γ diffeomorphism of a closed Riemannian manifold, and we show that they always admit an asymptotic local product structure. This is a direct application of the notion of tubular dimension which we introduce and study in the manuscript. As an additional application we prove a bound on any two consecutive conditional entropies in terms of volume growth.