Elsevier, Journal of Differential Equations, 4(254), p. 1800-1832, 2013
DOI: 10.1016/j.jde.2012.11.007
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We consider sliding motion, in the sense of Filippov, on a discontinuity surface Σ of co-dimension 2. We characterize, and restrict to, the case of Σ being attractive through sliding. In this situation, we show that a certain Filippov sliding vector field fFfF (suggested in Alexander and Seidman, 1998 [2], di Bernardo et al., 2008 [6], Dieci and Lopez, 2011 [10]) exists and is unique. We also propose a characterization of first order exit conditions, clarify its relation to generic co-dimension 1 losses of attractivity for Σ, and examine what happens to the dynamics on Σ for the aforementioned vector field fFfF. Examples illustrate our results.