Regularization of discontinuous foliations: Blowing up and sliding conditions via Fenichel theory
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2017-12-15
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Panazzolo, Daniel
da Silva, Paulo R. [UNESP]
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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 discontinuity 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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Journal of Differential Equations, v. 263, n. 12, p. 8362-8390, 2017.