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<p>Based on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-metric, we introduce the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-estimation measure-theoretic restricted sensitivity and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-estimation topological restricted sensitivity. For a given topological dynamical system, we relate the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-estimation measure-theoretic and topological asymptotic rates to the <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-estimation Brin-Katok local entropy and the <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-estimation topological entropy. Besides, we calculate these asymptotic rates for a class of symbolic systems.</p>

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\(\alpha \)-estimation time-restricted sensitivity and entropies

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Yunxiang Xie

摘要

Based on \(\alpha \) α -metric, we introduce the \(\alpha \) α -estimation measure-theoretic restricted sensitivity and \(\alpha \) α -estimation topological restricted sensitivity. For a given topological dynamical system, we relate the \(\alpha \) α -estimation measure-theoretic and topological asymptotic rates to the \(\alpha \) α -estimation Brin-Katok local entropy and the \(\alpha \) α -estimation topological entropy. Besides, we calculate these asymptotic rates for a class of symbolic systems.