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Morse inequalities for a dynamical system. (English) Zbl 0100.29701

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[1] A. A. Andronov and L. S. Pontrjagin, Systèmes grossiers, Dokl. Akad. Nauk vol. 14 (1937) pp. 247-250. · JFM 63.0728.01
[2] Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. · Zbl 0064.33002
[3] H. F. DeBaggis, Dynamical systems with stable structures, Contributions to the Theory of Nonlinear Oscillations, vol. II, Princeton University Press, Princeton, 1952, pp. 37 – 59. · Zbl 0047.33002
[4] L. È. Èl\(^{\prime}\)sgol\(^{\prime}\)c, An estimate for the number of singular points of a dynamical system defined on a manifold, Mat. Sbornik N.S. 26(68) (1950), 215 – 223 (Russian).
[5] R. K. Lashof and S. Smale, Self-intersections of immersed manifolds, J. Math. Mech. 8 (1959), 143 – 157. · Zbl 0093.37501
[6] Solomon Lefschetz, Differential equations: geometric theory, Pure and Applied Mathematics. Vol. VI, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. · Zbl 0080.06401
[7] Daniel C. Lewis Jr., Invariant Manifolds Near an Invariant Point of Unstable Type, Amer. J. Math. 60 (1938), no. 3, 577 – 587. · Zbl 0019.06501 · doi:10.2307/2371599 · doi.org
[8] Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. · Zbl 0011.02802
[9] M. M. Peixoto, On structural stability, Ann. of Math. (2) 69 (1959), 199 – 222. · Zbl 0084.08403 · doi:10.2307/1970100 · doi.org
[10] Everett Pitcher, Inequalities of critical point theory, Bull. Amer. Math. Soc. 64 (1958), 1 – 30. · Zbl 0083.32704
[11] Georges Reeb, Sur certaines propriétés topologiques des trajectoires des systèmes dynamiques, Acad. Roy. Belgique. Cl. Sci. Mém. Coll. in 8^\deg 27 (1952), no. 9, 64 (French). · Zbl 0048.32903
[12] S. Smale, On structural stability, to appear. · Zbl 0121.17906
[13] Shlomo Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math. 79 (1957), 809 – 824. · Zbl 0080.29902 · doi:10.2307/2372437 · doi.org
[14] René Thom, Sur une partition en cellules associée à une fonction sur une variété, C. R. Acad. Sci. Paris 228 (1949), 973 – 975 (French). · Zbl 0034.20802
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