Artículos de revistas
Regularization Of Discontinuous Vector Fields On ℝ3 Via Singular Perturbation
Registro en:
Journal Of Dynamics And Differential Equations. , v. 19, n. 2, p. 309 - 331, 2007.
10407294
10.1007/s10884-006-9057-7
2-s2.0-34249880482
Autor
Llibre J.
Da Silva P.R.
Teixeira M.A.
Institución
Resumen
Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields. © Springer Science+Business Media, LLC 2007. 19 2 309 331 Battelli, F., Palmer, K.J., Singular perturbations, transversality, and Sil'nikov saddle-focus homoclinic orbits (2003) J. Dyn. Diff. Equat, 15, pp. 357-425 Buzzi, C., Silva, P.R., Teixeira, M.A., Singular perturbation problems for time reversible systems (2005) Proc. Am. Math. Sac, 133, pp. 3323-3331 Dumortier, F., and Roussarie, R. (1996). Canard cycles and center manifolds. Mem. Am. Math. Soc. 121 pp. X + 100Fenichel, N., Geometric singular perturbation theory for ordinary differential equations (1979) J. Diff. Equat, 31, pp. 53-98 Filippov, A.F., Differential Equations with Discontinuous Righthand Sides, Mathematics and its Applications (1988) Soviet Series, , Kluwer Academic Publishers, Dordrecht Kozlova, V.S., (1984) Roughness of a discontinuous system, vestn, 5, pp. 16-20. , Mosk. Univ, Math Llibre, J., Teixeira, M.A., Regularization of discontinuous vector fields in dimension three (1997) Discrete Contin. Dyn. Syst, 3, pp. 235-241 Sotomayor, J., Teixeira, M.A., Regularization of discontinuous vector fields (1996) Proceedings of the International Conference on Differential Equations, pp. 207-223. , Lisboa, pp Sotomayor, J., Teixeira, M.A., Vector fields near the boundary of a 3-manifold (1988) Lecture Notes in Mathematics, 1331, pp. 169-195. , Springer-Verlag, Berlin, pp Szmolyan, P., Transversal heteroclinic and homoclinic orbits in singular perturbation problems (1991) J. Diff. Equat, 92, pp. 252-281 Teixeira, M.A., Generic singularities of discontinuous vector fields (1991) An. Acad. Bras. Cienc, 53, pp. 257-260 Teixeira, M.A., Stability conditions for discontinuous vector fields (1990) J. Diff. Equat, 88, pp. 15-24