Sliding vector fields via slow-fast systems

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

Research output: Contribution to journalArticleResearchpeer-review

28 Citations (Scopus)

Abstract

This paper concerns differential equation systems on ℝn with discontinuous right-hand sides. We deal with non-smooth vector fields in ℝ having a codimension-one submanifold M as its discontinuity set. After a regularization of a such system and a global blow-up we are able to bring out some results that bridge the space between discontinuous systems and singularly perturbed smooth systems.
Original languageEnglish
Pages (from-to)851-869
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Volume15
Issue number5
Publication statusPublished - 1 Dec 2008

Keywords

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

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