Smooth invariant curves of singularities of vector fields on
Annales de l'I.H.P. Analyse non linéaire (1986)
- Volume: 3, Issue: 2, page 111-183
- ISSN: 0294-1449
Access Full Article
topHow to cite
topBonckaert, Patrick. "Smooth invariant curves of singularities of vector fields on $\mathbb {R}^3$." Annales de l'I.H.P. Analyse non linéaire 3.2 (1986): 111-183. <http://eudml.org/doc/78109>.
@article{Bonckaert1986,
author = {Bonckaert, Patrick},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {invariant manifold; theory of singularities of vector fields},
language = {eng},
number = {2},
pages = {111-183},
publisher = {Gauthier-Villars},
title = {Smooth invariant curves of singularities of vector fields on $\mathbb \{R\}^3$},
url = {http://eudml.org/doc/78109},
volume = {3},
year = {1986},
}
TY - JOUR
AU - Bonckaert, Patrick
TI - Smooth invariant curves of singularities of vector fields on $\mathbb {R}^3$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1986
PB - Gauthier-Villars
VL - 3
IS - 2
SP - 111
EP - 183
LA - eng
KW - invariant manifold; theory of singularities of vector fields
UR - http://eudml.org/doc/78109
ER -
References
top- [Ar] V. Arnold, Équations différentielles ordinaires, Éditions Mir, Moscou, 1974. Zbl0296.34002MR990889
- [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. Zbl0171.44404MR240836
- [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. Zbl0584.58009
- [Be] G.R. Belitskii, Equivalence and Normal Forms of Germs of Smooth Mappings. Russian Math. Surveys, t. 33, 1978, p. 107-177. Zbl0398.58009MR490708
- [Br] H.W. Broer, Formal Normal Form Theorems for Vector Fields and some Consequences in the Volume Preserving Case, in: Dynamical Systems and Turbulence, Warwick1980, Lecture Notes in Math., t. 898. 1981. Zbl0504.58031
- [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. Zbl0464.58001MR635782
- [Di] J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1969. Zbl0176.00502MR349288
- [Du1] F. Dumortier, Singularities of Vector Fields on the Plane. Journal of Diff. Eq., t. 23, 1977, p. 53-106. Zbl0346.58002MR650816
- [Du2] F. Dumortier, Singularities of Vector Fields. Monografias de Matematica, t. 32, IMPA, Rio de Janeiro, 1978. MR526571
- [D. R. R.] F. Dumortier, P.R. Rodrigues and R. Roussarie, Germs of Diffemorphisms in the Plane. Lecture Notes in Math., t. 902, 1981. Zbl0502.58001MR653474
- [Go] R.E. Gomory, Trajectories tending to a Critical Point in 3-space. Annals of Math., t. 61, 1955, p. 140-153. Zbl0068.29703MR67276
- [Gu] J. Guckenheimer and P. Holmes, Nonlinear oscillations, Dynamical Systems and Bifurcations, Springer-Verlag, New York, 1983. Zbl0515.34001MR709768
- [Ha] P. Hartman, Ordinary Differential Equations. Wiley and Sons, New York. Zbl0125.32102MR171038
- [H. P. S.] M.W. Hirsch, C.C. Pugh and M. Shub, Invariant Manifolds. Lecture Notes in Math., t. 583, 1977. Zbl0355.58009MR501173
- [Ir] M.C. Irwin, Smooth Dynamical Systems, Academic Press, New York, 1980. Zbl0465.58001MR586942
- [Ke] A. Kelley, The Stable, Center-Stable, Center, Center-Unstable, Unstable Manifolds. Journal of Diff. Eq., t. 3, 1967, p. 546-570. Zbl0173.11001MR221044
- [M. M.] J. E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications, Springer-Verlag, New York, 1976. Zbl0346.58007MR494309
- [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. Zbl0089.29502MR121520
- [P. M.] J. Palis and W. De Melo, Geometric Theory of Dynamical Systems, Springer-Verlag, New York, 1982. Zbl0491.58001MR669541
- [Sh] D.S. Shafer, Singularities of Gradient Vectorfields in R3. Journal of Diff. Eq., t. 47, 1983, p. 317-326. Zbl0468.58017MR692834
- [Sm] D. Smart, Fixed point theorems. Cambridge University Press, 1974. Zbl0297.47042MR467717
- [Ta] F. Takens, Singularities of Vector Fields. Publ. Math. IHES, t. 43, 1974, p. 47-100. Zbl0279.58009MR339292
- [We] J.C. Wells, Invariant Manifolds of Non-Linear Operators. Pacific Journal of Math., t. 62, 1976, p. 285-293. Zbl0343.58010MR418164
- [Ya] S. Yamamuro, Differential calculus in topological linear spaces. Lecture Notes in Math., t. 374, 1974. Zbl0276.58001MR488118
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.