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<p>For every Lipschitz random dynamical system <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varphi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation> in a compact metric space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((\mathscr {Y},d)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">Y</mi> <mo>,</mo> <mi>d</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, associated with a Lebesgue space <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((\mathscr {Q}, \mathscr {F}, \mathbb {P})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">Q</mi> <mo>,</mo> <mi mathvariant="script">F</mi> <mo>,</mo> <mi mathvariant="double-struck">P</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, a concept of linear random cocycle for finite-dimensional space and Banach space were introduced in the context. We demonstrate that the Oseledets subspaces, as derived from the Multiplicative Ergodic Theorem, exhibit Hölder continuity over sets with measures nearly reaching 1.</p>

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Hölder continuity of Oseledets subspaces for linear random cocycle

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Peirong Li,
  • Zhiming Li

摘要

For every Lipschitz random dynamical system \(\varphi \) φ in a compact metric space \((\mathscr {Y},d)\) ( Y , d ) , associated with a Lebesgue space \((\mathscr {Q}, \mathscr {F}, \mathbb {P})\) ( Q , F , P ) , a concept of linear random cocycle for finite-dimensional space and Banach space were introduced in the context. We demonstrate that the Oseledets subspaces, as derived from the Multiplicative Ergodic Theorem, exhibit Hölder continuity over sets with measures nearly reaching 1.