Vector fields in the vicinity of a circle of critical points

Vector fields in the vicinity of a circle of critical points
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by J.-F. Mattei and M. A. Teixeira PDF

Trans. Amer. Math. Soc. 297 (1986), 369-381 Request permission

In this paper the ${C^S}$-conjugacy between vector fields on ${{\mathbf {R}}^2}$ having a circle of critical points is studied.

References

Freddy Dumortier, Singularities of vector fields on the plane, J. Differential Equations 23 (1977), no. 1, 53–106. MR 650816, DOI 10.1016/0022-0396(77)90136-X
F. Dumortier and R. Roussarie, Germes de difféomorphismes et de champs de vecteurs en classe de différentiabilité finie, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 1, 195–267 (French). MR 698855
Jack K. Hale, Ordinary differential equations, Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. MR 0419901
Floris Takens, Forced oscillations and bifurcations, Applications of global analysis, I (Sympos., Utrecht State Univ., Utrecht, 1973) Comm. Math. Inst. Rijksuniv. Utrecht, No. 3-1974, Math. Inst. Rijksuniv. Utrecht, Utrecht, 1974, pp. 1–59. MR 0478235
Floris Takens, Normal forms for certain singularities of vectorfields, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 2, 163–195 (English, with French summary). MR 365620

A topological invariant for discontinuous vector fields

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