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Singularities of vector fields on the plane. (English) Zbl 0346.58002

MSC:
58C25 Differentiable maps on manifolds
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[1] Abraham, R; Robbin, J, Transversal mappings and flows, (1967), Benjamin New York · Zbl 0171.44404
[2] Andronov, A.A; Leontovich, E.A; Gordon, I.I; Maier, A.G, Theory of bifurcations of dynamical systems on a plane, (1971), Israel Program for Sci. Trans
[3] Argémi, J, Sur LES points singuliers multiples de systèmes dynamiques dans \(R\)^{2}, Ann. mat. pura appl. ser IV, 79, 35-70, (1968) · Zbl 0203.39802
[4] Argémi, J, Points singuliers non élémentaires de quelques classes de systèmes dynamiques plans, Ann. mat. pura appl. ser. IV, 89, 321-352, (1971) · Zbl 0298.34021
[5] Bröcker, Th, Differenzierbare abbildungen. einfuhrung in die lokale theorie, (1972), Fachbereich Mathematic der Universität Regensburg Regensburg, W. Germany
[6] Cartan, H, Topologie différentielle, ()
[7] Coleman, C, Equivalence of planar dynamical and differential systems, J. differential equations, 1, 222-233, (1965), (2) · Zbl 0135.30704
[8] De Baggis, H.F, Dynamical systems with stable structures, ()
[9] Dulac, M.H, Sur LES cycles limites, Bull. soc. math. France, 51, 45-188, (1923) · JFM 49.0304.01
[10] Grobman, D, Homeomorphisms of systems of differential equations, Dokl. akad. nauk., 128, (1965)
[11] Hartman, P, Ordinary differential equations, (1964), Wiley New York · Zbl 0125.32102
[12] Hartman, P, On the local linearization of differential equations, (), 568-573 · Zbl 0115.29801
[13] Hirsch, M; Pugh, C.C, Stable manifolds and hyperbolic sets, () · Zbl 0215.53001
[14] Hirsch, M; Pugh, C.C; Shub, M, Invariant manifolds, Bull. amer. math. soc., 76, 1015-1019, (1970) · Zbl 0226.58009
[15] Il’Yashenko, Y.S, Algebraic nonsolvability and almost algebraic solvability of the center-focus problem, Functional anal. appl., 197-202, (1972) · Zbl 0267.34025
[16] Kelley, A, (), Appendix C
[17] Lang, S, Introduction to differentiable manifolds, (1967), Interscience New York
[18] Levine, H.I, ()
[19] Malgrange, B, Ideals of differentiable functions, (1966), Oxford Univ. Press Oxford
[20] Malgrange, B, ()
[21] Mather, J, Stability of C∞ mappings III: finitely determined map-germs, Publ. math. I.H.E.S., 35, (1968) · Zbl 0159.25001
[22] {\scJ. Mather}, Unpublished notes.
[23] Munkrès, J, Elementary differential topology, () · Zbl 0107.17201
[24] Narasimhan, N, Analysis on real and complex manifolds, (1968), North-Holland Amsterdam · Zbl 0188.25803
[25] Nemytskii, V.V; Stepanov, V.V, Qualitative theory of differential equations, (1960), Princeton Univ. Press Princeton, N.J · Zbl 0089.29502
[26] Peixoto, M, On structural stability, Ann. of math., 69, 199-222, (1959) · Zbl 0084.08403
[27] Peixoto, M, Structural stability on two dimensional manifolds, Topology, 1, 101-120, (1962) · Zbl 0107.07103
[28] Pugh, C.C, On a theorem of P. hartman, Amer. J. math., 91, 363-367, (1969) · Zbl 0197.20701
[29] Pugh, C.C; Shub, M, Linearization of normally hyperbolic diffeomorphisms and flows, Invent. math., 10, 187-198, (1970) · Zbl 0206.25802
[30] Seidenberg, A, A new decision method for elementary algebra, Ann. of math., 60, 365-374, (1954) · Zbl 0056.01804
[31] Seidenberg, A, Elements of the theory of algebraic curves, (1968), Addison-Wesley Reading, Mass · Zbl 0159.33303
[32] Smale, S, Differentiable dynamical systems, Bull. amer. math. soc., 73, 747-817, (1967) · Zbl 0202.55202
[33] Smale, S, Stable manifolds for differentiable equations and diffeomorphisms, Annali scuola norm. Pisa, serie III, 17, 97-116, (1963) · Zbl 0113.29702
[34] Sotomayor, J, Generic one-parameter families of vector fields on two dimensional manifolds, Publ. math. I.H.E.S., 43, (1974) · Zbl 0279.58008
[35] Takens, F, Partially hyperbolic fixed points, Topology, 10, 133-147, (1971) · Zbl 0214.22901
[36] Takens, F, Singularities of functions and vector fields, Nieuw arch. wisk., 20, 107-130, (1972), (3) · Zbl 0237.58012
[37] Takens, F, Singularities of vector fields, Publ. math. I.H.E.S., 43, (1974)
[38] Tarski, A, A decision procedure for elementary algebra and geometry, (1951), Univ. California Press Berkeley · Zbl 0044.25102
[39] Thom, R, Stabilité structurelle et morphogénèse, (1972), Benjamin New York
[40] Tougeron, Idéaux de functions différentiables, (1972), Springer-Verlag Berlin · Zbl 0251.58001
[41] Wall, C.T.C, ()
[42] Whitney, H, Elementary structure of real algebraic varieties, Ann. of math., 66, 545-556, (1957) · Zbl 0078.13403
[43] Lyapunov, A.M, Stability of motion, (), Transl. by F. Abramovici and M. Shimshoni · Zbl 0161.06303
[44] Dumortier, F, Singularités de champs de vecteurs sur le plan. germes déterminés par un jet d’ordre fini, C. R. acad. sci. Paris ser. A, 278, 497-500, (1974) · Zbl 0294.58005
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