Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
MathSciNet review: 849485
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


References [Enhancements On Off] (What's this?)

  • [1] Freddy Dumortier, Singularities of vector fields on the plane, J. Differential Equations 23 (1977), no. 1, 53–106. MR 0650816 (58 #31276)
  • [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 (84m:58114)
  • [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 (54 #7918)
  • [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 (57 #17720)
  • [5] Floris Takens, Normal forms for certain singularities of vectorfields, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 2, 163–195 (English, with French summary). Colloque International sur l’Analyse et la Topologie Différentielle (Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg, 1972). MR 0365620 (51 #1872)
  • [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.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F14, 34C35

Retrieve articles in all journals with MSC: 58F14, 34C35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0849485-4
PII: S 0002-9947(1986)0849485-4
Keywords: Vector field, critical point, conjugacy
Article copyright: © Copyright 1986 American Mathematical Society