Keywords
- Periodic Orbit
- Singular Point
- Cusp Point
- Elliptic Point
- Hyperbolic Saddle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
N. Bautin., On the number of limit cycles appearing with variations of the coefficients from an equilibrium state of the type of a focus or a center, Math. Sb. (N.S.) 30 (72) (1952), p. 181–196.
J. Ecalle., J. Martinet., R. Moussu., J.P. Ramis., Non-accumulation de cycles limites, C.R.A.S., t. 304, série I, no 14 (1987), (I): p. 375–378, (II): p. 431–434.
J.P. Francoise and C.C. Pugh., Keeping track of limit cycles, Journal of Diff. Eq. 65 (1986) p. 139–157.
Yu. Il'yasenko., Ycπ. Math. Hayk., 42, 3 (1987), p. 223.
K. Kuratowski., Topology, Vol. II, Academic Press, N.Y. London (1966).
[R1] R. Roussarie., On the number of limit cycles which appear by perturbation of a separatrix loop of planar vector fields. Bol. Soc. Math. Bras. Vol. 17, no 2 (1986) p. 67–101.
[R2] R. Roussarie., Déformations génériques des cusps. (To appear in Astérisque: Journées Singulieres, Dijon, 1985).
[R3] R. Roussarie., Cyclicité finie des lacets et des points cuspidaux. (Preprint)
J. Ch. Yoccoz., Non-accumulation des cycles limites, Séminaire Bourbaki 40e. Année, 1987–88, no 690.
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Roussarie, R. (1988). A note on finite cyclicity property and Hilbert's 16th. Problem. In: Bamón, R., Labarca, R., Palis, J. (eds) Dynamical Systems Valparaiso 1986. Lecture Notes in Mathematics, vol 1331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083072
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DOI: https://doi.org/10.1007/BFb0083072
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