Smooth invariant curves of singularities of vector fields on 3
Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986) no. 2, pp. 111-183.
@article{AIHPC_1986__3_2_111_0,
     author = {Bonckaert, Patrick},
     title = {Smooth invariant curves of singularities of vector fields on $\mathbb {R}^3$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {111--183},
     publisher = {Gauthier-Villars},
     volume = {3},
     number = {2},
     year = {1986},
     mrnumber = {837232},
     zbl = {0597.58021},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1986__3_2_111_0/}
}
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Bonckaert, Patrick. Smooth invariant curves of singularities of vector fields on $\mathbb {R}^3$. Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986) no. 2, pp. 111-183. http://archive.numdam.org/item/AIHPC_1986__3_2_111_0/

[Ar] V. Arnold, Équations différentielles ordinaires, Éditions Mir, Moscou, 1974. | MR | Zbl

[A. M.] R. Abraham and J.E. Marsden, Foundations of Mechanics. Benjamin, London,

[A. R.] R. Abraham and J. Robbin, Transversal Mappings and Flows. Appendix by Kelley, Benjamin, New York, 1967. | MR | Zbl

[B. D.] P. Bonckaert and F. Dumortier, Smooth Invariant Curves for Germs of Vector Fields in R3 whose Linear Part Generates a Rotation, to appear in Journal of Differential Equations. | Zbl

[Be] G.R. Belitskii, Equivalence and Normal Forms of Germs of Smooth Mappings. Russian Math. Surveys, t. 33, 1978, p. 107-177. | MR | Zbl

[Br] H.W. Broer, Formal Normal Form Theorems for Vector Fields and some Consequences in the Volume Preserving Case, in: Dynamical Systems and Turbulence, Warwick 1980, Lecture Notes in Math., t. 898. 1981. | Zbl

[Cam] M.I.T. Camacho, A contribution to the Topological Classification of Homogeneous Vector Fields in R3 (preprint).

[Car] J. Carr, Applications of Centre Manifold Theory, Springer Verlag, New York, 1981. | MR | Zbl

[Di] J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1969. | MR | Zbl

[Du1] F. Dumortier, Singularities of Vector Fields on the Plane. Journal of Diff. Eq., t. 23, 1977, p. 53-106. | MR | Zbl

[Du2] F. Dumortier, Singularities of Vector Fields. Monografias de Matematica, t. 32, IMPA, Rio de Janeiro, 1978. | MR

[D. R. R.] F. Dumortier, P.R. Rodrigues and R. Roussarie, Germs of Diffemorphisms in the Plane. Lecture Notes in Math., t. 902, 1981. | MR | Zbl

[Go] R.E. Gomory, Trajectories tending to a Critical Point in 3-space. Annals of Math., t. 61, 1955, p. 140-153. | MR | Zbl

[Gu] J. Guckenheimer and P. Holmes, Nonlinear oscillations, Dynamical Systems and Bifurcations, Springer-Verlag, New York, 1983. | MR | Zbl

[Ha] P. Hartman, Ordinary Differential Equations. Wiley and Sons, New York. | MR | Zbl

[H. P. S.] M.W. Hirsch, C.C. Pugh and M. Shub, Invariant Manifolds. Lecture Notes in Math., t. 583, 1977. | MR | Zbl

[Ir] M.C. Irwin, Smooth Dynamical Systems, Academic Press, New York, 1980. | MR | Zbl

[Ke] A. Kelley, The Stable, Center-Stable, Center, Center-Unstable, Unstable Manifolds. Journal of Diff. Eq., t. 3, 1967, p. 546-570. | MR | Zbl

[M. M.] J. E. Marsden and M. Mccracken, The Hopf Bifurcation and Its Applications, Springer-Verlag, New York, 1976. | MR | Zbl

[Na] N. Narasimham, Analysis on Real and Complex Manifolds, North-Holland, Amsterdam. 1968.

[N. S.] V.V. Nemytskh and V.V. Stepanov, Qualitative theory of Differential Equations. Princeton, Princeton University Press, 1960. | MR | Zbl

[P. M.] J. Palis and W. De Melo, Geometric Theory of Dynamical Systems, Springer-Verlag, New York, 1982. | MR | Zbl

[Sh] D.S. Shafer, Singularities of Gradient Vectorfields in R3. Journal of Diff. Eq., t. 47, 1983, p. 317-326. | MR | Zbl

[Sm] D. Smart, Fixed point theorems. Cambridge University Press, 1974. | MR | Zbl

[Ta] F. Takens, Singularities of Vector Fields. Publ. Math. IHES, t. 43, 1974, p. 47-100. | Numdam | MR | Zbl

[We] J.C. Wells, Invariant Manifolds of Non-Linear Operators. Pacific Journal of Math., t. 62, 1976, p. 285-293. | MR | Zbl

[Ya] S. Yamamuro, Differential calculus in topological linear spaces. Lecture Notes in Math., t. 374, 1974. | MR | Zbl