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<p>We study the asymptotic behaviour of discrete time set-valued dynamical systems defined by difference inclusions. Notions as limit sets, invariant or attractors sets are defined in terms of set-valued analysis and relations with different concepts of stable set (in the Lyapunov sense) are established. In this brief paper, we present applications of set-valued analysis to the dynamical system theory and provide a foundational theory in terms of stability analysis.</p>

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An underlying theory of multifunctions in discrete-time set-valued dynamical systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月19日

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  • Elvira Hernández,
  • Juan Perán

摘要

We study the asymptotic behaviour of discrete time set-valued dynamical systems defined by difference inclusions. Notions as limit sets, invariant or attractors sets are defined in terms of set-valued analysis and relations with different concepts of stable set (in the Lyapunov sense) are established. In this brief paper, we present applications of set-valued analysis to the dynamical system theory and provide a foundational theory in terms of stability analysis.