Vector fields in the vicinity of a circle of critical points
Authors:
J.-F. Mattei and M. A. Teixeira
Journal:
Trans. Amer. Math. Soc. 297 (1986), 369-381
MSC:
Primary 58F14; Secondary 34C35
DOI:
https://doi.org/10.1090/S0002-9947-1986-0849485-4
MathSciNet review:
849485
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper the -conjugacy between vector fields on
having a circle of critical points is studied.
- [1] Freddy Dumortier, Singularities of vector fields on the plane, J. Differential Equations 23 (1977), no. 1, 53–106. MR 650816, https://doi.org/10.1016/0022-0396(77)90136-X
- [2] 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
- [3] Jack K. Hale, Ordinary differential equations, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. Pure and Applied Mathematics, Vol. XXI. MR 0419901
- [4] Floris Takens, Forced oscillations and bifurcations, Applications of global analysis, I (Sympos., Utrecht State Univ., Utrecht, 1973) Math. Inst. Rijksuniv. Utrecht, Utrecht, 1974, pp. 1–59. Comm. Math. Inst. Rijksuniv. Utrecht, No. 3-1974. MR 0478235
- [5] 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
- [6] M. A. Teixeira, A topological invariant for discontinuous vector fields, Nonlinear Analysis: Theory, Methods and Applications (to appear).
- [7] S. P. Tokarev, Smooth equivalence of differential-equation systems in the plane in the case of a noncoarse focus, Differentisial'nye Uravnenija 13 (1977), 613-617.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1986-0849485-4
Keywords:
Vector field,
critical point,
conjugacy
Article copyright:
© Copyright 1986
American Mathematical Society