Regularization of discontinuous vector fields on ℝ3 via singular perturbation

Jaume Llibre, Paulo R. Da Silva, Marco A. Teixeira

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91 Citations (Scopus)


Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields. © Springer Science+Business Media, LLC 2007.
Original languageEnglish
Pages (from-to)309-331
JournalJournal of Dynamics and Differential Equations
Publication statusPublished - 1 Jun 2007


  • Discontinuous vector fields
  • Regularization
  • Singular perturbation
  • Vector fields


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