Work

Conley Index of Limit Cycles in Filippov Vector Fields

Year: 2026

Type: preprint

Abstract: Within the framework of multivalued dynamical systems, we compute the Conley index for a class of limit cycles in planar Filippov systems. We classify these cycles according to their interaction with the switching manifold, including crossing, sliding, and mixed regimes. Using the Conley index for multivalued admissible maps developed by Mrozek, we construct the appropriate index pairs and determine the corresponding indices for each class. These computations enlarge the class of Filippov invariant sets for which the Conley index is known and extend previous results on low-codimension singularities to periodic dynamics.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.14876

Authors: Cândido, Letícia, Lima, Dahisy, de Rezende, Ketty

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Award: G7317222892

OpenAlex ID: W7221786990

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