Abstract
We introduce the notion of semi-local structural stability which detects if a nonsmooth system is structurally stable around the switching manifold. More specifically, we characterize the semi-local structurally stable systems in a class of Filippov systems on a compact 3-manifold which has a simply connected switching manifold.
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References
M. Guardia, T.M. Seara, M.A. Teixeira, Generic bifurcations of low codimension of planar Filippov systems. J. Differ. Equ. 250, 1967–2023 (2011)
M.C. Peixoto, M.M. Peixoto, Structural stability in the plane with enlarged boundary conditions. An. Acad. Bras. Ciencias 31 (1959)
M.A. Teixeira, Stability conditions for discontinuous vector fields. J. Differ. Equ. 88(1), 15–29 (1990)
S.M. Vishik, Vector fields near the boundary of a manifold. Vestnik Moskovskogo Universiteta Mathematika 27(1), 21–28 (1972)
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Gomide, O.M.L., Teixeira, M.A., Martins, R.M. (2017). On Semi-local Structural Stability of Filippov Systems. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_15
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DOI: https://doi.org/10.1007/978-3-319-55642-0_15
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