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<p>This paper explores the definition of the Conley index for Filippov vector fields, building on the foundational work of Mrozek. Mrozek developed a framework for applying the Conley index to admissible multi-valued flows. We adapt Mrozek’s construction to ensure the existence of topological pairs for isolated invariant sets in planar Filippov systems obtaining a classification for low codimension singularities.</p>

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Conley Index for Filippov Planar Vector Fields

  • 期刊论文

  • 发表日期：

    2026年5月27日

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  • L. Cândido,
  • D. V. S. Lima,
  • K. A. de Rezende

摘要

This paper explores the definition of the Conley index for Filippov vector fields, building on the foundational work of Mrozek. Mrozek developed a framework for applying the Conley index to admissible multi-valued flows. We adapt Mrozek’s construction to ensure the existence of topological pairs for isolated invariant sets in planar Filippov systems obtaining a classification for low codimension singularities.