Regularization of Discontinuous Vector Fields on $${\mathbb{R}^3}$$ via Singular Perturbation

@article{Llibre2007RegularizationOD,
  title={Regularization of Discontinuous Vector Fields on \$\$\{\mathbb\{R\}^3\}\$\$ via Singular Perturbation},
  author={J. Llibre and Paulo Ricardo da Silva and M. A. Teixeira},
  journal={Journal of Dynamics and Differential Equations},
  year={2007},
  volume={19},
  pages={309-331}
}
  • J. Llibre, Paulo Ricardo da Silva, M. A. Teixeira
  • Published 2007
  • Mathematics
  • Journal of Dynamics and Differential Equations
  • 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. 
    74 Citations
    Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation
    • 39
    • PDF
    Regularizing Piecewise Smooth Differential Systems: Co-Dimension $$2$$ Discontinuity Surface
    • 16
    • PDF
    Synchronization and Non-Smooth Dynamical Systems
    • 1
    • PDF

    References

    SHOWING 1-9 OF 9 REFERENCES
    Regularization Of Discontinuous Vector Fields In Dimension Three
    • 61
    Stability conditions for discontinuous vector fields
    • 88
    Transversal heteroclinic and homoclinic orbits in singular perturbation problems
    • 102
    • Highly Influential
    • PDF
    Differential Equations with Discontinuous Righthand Sides
    • 5,180
    • PDF
    Geometric singular perturbation theory for ordinary differential equations
    • 1,649
    • Highly Influential
    • PDF
    Canard Cycles and Center Manifolds
    • 376