Nonsingular quadratic differential equations in the plane
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- by M. I. T. Camacho and C. F. B. Palmeira
- Trans. Amer. Math. Soc. 301 (1987), 845-859
- DOI: https://doi.org/10.1090/S0002-9947-1987-0882718-8
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Erratum: Trans. Amer. Math. Soc. 307 (1988), 431.
Abstract:
We consider the problem of determining the number of inseparable leaves of nonsingular polynomial differential equations of degree two. As a corollary of a classification theorem for the foliation defined by these equations, we prove that this number is at most 2.References
- V. Arnold, Chapitres supplémentaires de la théorie des équations différentielles ordinaires, Éditions de Moscou.
- Carmen Chicone and Jing Huang Tian, On general properties of quadratic systems, Amer. Math. Monthly 89 (1982), no. 3, 167–178. MR 645790, DOI 10.2307/2320199
- Freddy Dumortier, Singularities of vector fields, Monografías de Matemática [Mathematical Monographs], vol. 32, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1978. MR 526571
- A. Gasull, Li Ren Sheng, and J. Llibre, Chordal quadratic systems, Proceedings of the seventh congress on differential equations and applications (Granada, 1984) Univ. Granada, Granada, 1985, pp. 169–174 (Spanish). MR 793765
- L. Markus, Topological types of polynomial differential equations, Trans. Amer. Math. Soc. 171 (1972), 157–178. MR 306634, DOI 10.1090/S0002-9947-1972-0306634-4
- Marie-Paule Muller, Quelques propriétés des feuilletages polynomiaux du plan, Bol. Soc. Mat. Mexicana (2) 21 (1976), no. 1, 6–14 (French). MR 501014
- Carlos Frederico Borges Palmeira, Open manifolds foliated by planes, Ann. of Math. (2) 107 (1978), no. 1, 109–131. MR 501018, DOI 10.2307/1971256 Sheng Li-Ren, Systèmes quadratiques et camposantes de Reeb, Publication de l’IRMA, Univ. de Strasbourg, 1984, 226/p-132.
- Stephen Schecter and Michael F. Singer, Planar polynomial foliations, Proc. Amer. Math. Soc. 79 (1980), no. 4, 649–656. MR 572321, DOI 10.1090/S0002-9939-1980-0572321-0 —, Singular points of planar vector fields, Lecture Notes in Math., vol. 819, Springer-Verlag, Berlin and New York.
- Floris Takens, Singularities of vector fields, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 47–100. MR 339292
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 301 (1987), 845-859
- MSC: Primary 58F18; Secondary 34C35
- DOI: https://doi.org/10.1090/S0002-9947-1987-0882718-8
- MathSciNet review: 882718