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REGULARIZATION OF DISCONTINUOUS FOLIATIONS: BLOWING UP AND SLIDING CONDITIONS VIA FENICHEL THEORY

Abstract : We study the regularization of an oriented 1-foliation F on M \ Σ where M is a smooth manifold and Σ ⊂ M is a closed subset, which can be interpreted as the discontinuity locus of F. In the spirit of Filippov's work, we define a sliding and sewing dynamics on the discon-tinuity locus Σ as some sort of limit of the dynamics of a nearby smooth 1-foliation and obtain conditions to identify whether a point belongs to the sliding or sewing regions.
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Daniel Panazzolo, Paulo da Silva. REGULARIZATION OF DISCONTINUOUS FOLIATIONS: BLOWING UP AND SLIDING CONDITIONS VIA FENICHEL THEORY. Journal of Differential Equations, Elsevier, 2017, 263 (12), pp.8362-8390. ⟨10.1016/j.jde.2017.08.042⟩. ⟨hal-02907170⟩

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