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<p>We suggest a method of discretization of the domain of dynamical systems based on observations. The method utilizes <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-entropy, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-capacity, and the introduced <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-information. It results in the partition of the system’s domain to the cells of equal diameters that allows representation of the system in the terms of discrete dynamics and its numerical analysis and modelling.</p>

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Information-Based Partitioning of the Dynamical System’s Domain

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月4日

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  • Eugene Kagan,
  • Alexander Novoselsky

摘要

We suggest a method of discretization of the domain of dynamical systems based on observations. The method utilizes \(\varepsilon \) ε -entropy, \(\varepsilon \) ε -capacity, and the introduced \(\varepsilon \) ε -information. It results in the partition of the system’s domain to the cells of equal diameters that allows representation of the system in the terms of discrete dynamics and its numerical analysis and modelling.