SIGMA]] (y) = (0, g(y)) is called sliding vector field.
The existence of sliding closed poly-trajectories depends of some inequalities which are related with: equilibrium position (real or virtual), the sign of derivative of the sliding vector field and the determinant of the matrices [A.
2] > 0, and the sliding vector field is given in (12).
2] = 0, then the sliding vector field is identically zero and this implies the non-existence of closed sliding poly-trajectories.
The sliding vector field associated to Z [member of] [[?
1 of  says that there exists a singular perturbation problem such that the sliding region is homeomorphic to the slow critical manifold and the sliding vector field is topologically equivalent to the reduced problem.
TEIXEIRA, Sliding vector fields via slow-fast systems, Bulletin of the Belgian Mathematical Society Simon Stevin 15-5 (2008), 851-869.