Generic one-parameter families of vector fields on two-dimensional manifolds
Publications Mathématiques de l'IHÉS, Volume 43 (1974), pp. 5-46.
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     title = {Generic one-parameter families of vector fields on two-dimensional manifolds},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {5--46},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {43},
     year = {1974},
     mrnumber = {339279},
     zbl = {0279.58008},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1974__43__5_0/}
}
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Sotomayor, Jorge. Generic one-parameter families of vector fields on two-dimensional manifolds. Publications Mathématiques de l'IHÉS, Volume 43 (1974), pp. 5-46. http://www.numdam.org/item/PMIHES_1974__43__5_0/

[1] G. F. Duff, Limit cycles and vector fields, Ann. of Math., vol. 57 (1953), 15-31. | MR | Zbl

[2] M. Urabe, Infinitesimal deformation of cycles, Jour. Sci. Hiroshima University, 1954, 37-53. | MR | Zbl

[3] L. Marcus and A. Aeppli, Integral equivalence of vector fields on manifolds and bifurcation of differential systems, American Journal of Math., vol. 85 (1963), 633-654. | MR | Zbl

[4] R. Sacker, Invariant surfaces and bifurcation of periodic solutions of ordinary differential equations, New York University, Courant Inst. Math. Sci. Tech. Rep. IMM-NYU 333, 1964.

[5] M. C. Peixoto and M. Peixoto, Structural Stability in the plane with enlarged boundary conditions, Ann. Acad. Bras. Sci., vol. 81 (1959), 135-160. | MR | Zbl

[6] M. Peixoto, An approximation theorem of Kupka and Smale, Jour. of Diff. Eq., vol. 3 (1967), 214-227. | MR | Zbl

[7] M. Peixoto, On structural stability, Ann. of Math., vol. 69 (1959), 199-222. | MR | Zbl

[8] M. Peixoto, Structural stability on two dimensional manifolds, Topology, vol. 1 (1962), 101-120. | MR | Zbl

[9] S. Smale, On dynamical Systems, Boletin de la Soc. Mat. Mexicana, vol. 66 (1960), 195-198. | MR | Zbl

[10] S. Smale, Differentiable dynamical Systems, BAMS, vol. 73 (1967), 747-817. | MR | Zbl

[11] S. Smale, Stable manifolds for differential equations and diffeomorphisms, Annali Scuola Normale de Pisa, serie III, XVII (1963), 97-116. | Numdam | MR | Zbl

[12] I. Kupka, Contribution à la théorie des champs génériques, Cont. to Diff. Eq., vol. 2 (1963), 451-487. | MR | Zbl

[13] A. Andronov and E. Leontovich, Sur la théorie de la variation de la structure qualitative de la division du plan en trajectoires, Dokl. Akad. Nauk., vol. 21 (1938), 427-430. | JFM | Zbl

[14] J. Sotomayor, Estabilidade estrutural de primeira ordem em variedades de Banach, Thesis, Rio de Janeiro, IMPA, 1964.

[15] S. Lang, Introduction to differentiable manifolds, New York, Interscience, 1962. | MR | Zbl

[16] R. Abraham, Transversal mappings and flows, New York, Benjamin, 1967. | MR | Zbl

[17] G. Sansone and R. Conti, Equazione differentiali non lineari, Rome, Ed. Cremonese, 1956. | Zbl

[18] E. Coddington and N. Levinson, Theory of ordinary differential equations, New York, McGraw Hill, 1955. | MR | Zbl

[19] P. Hartman, Ordinary differential equations, New York, John Wiley, 1964. | MR | Zbl

[20] C. Pugh, The closing lemma, Amer. J. Math., vol. 89 (1967), 956-1009. | MR | Zbl

[21] W. S. Loud, Behavior of the period of solutions of certain plane autonomous systems near centers, Contr. to Diff. Eq., vol. 3 (1963), 21-36. | MR | Zbl