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The stable, center-stable, center, center-unstable, unstable manifolds. (English) Zbl 0173.11001


MSC:

34Cxx Qualitative theory for ordinary differential equations
37C10 Dynamics induced by flows and semiflows

Citations:

Zbl 0163.32804
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References:

[1] Coddington, E.; Levinson, N., Theory of Ordinary Differential Equations (1955), McGraw-Hill: McGraw-Hill New York · Zbl 0064.33002
[2] Bogoliubov, N.; Mitropolsky, Y., Asymptotic Methods in the Theory of Non-linear Oscillations (1961), Gordon and Breach: Gordon and Breach New York · Zbl 0151.12201
[3] Diliberto, S. P., Perturbation theorems for periodic surfaces, Rend. Circ. Mat. Palermo, 10, 1-51 (1961) · Zbl 0109.31401
[4] Hale, J., On the method of Krylov-Bogoliubov-Mitropolski for the existence of integral manifolds of perturbed differential systems, (Symposium Internacional de Ecuaciones Diferenciales Ordinarias (1961), University of Mexico), 51-57 · Zbl 0121.07403
[5] Hale, J., Integral manifolds of perturbed differential systems, Ann. Math., 73, 496-531 (1961) · Zbl 0163.32804
[6] Krylov, N.; Bogoliubov, N., The application of methods of nonlinear mechanics to the theory of stationary oscillations, (Publication No. 8 of the Ukrainian Academy of Science (1934)), (in Russian) · Zbl 0063.03382
[7] Levinson, N., Small periodic perturbations of an autonomous system with a stable orbit, Ann. Math., 52, 727-738 (1950) · Zbl 0038.24903
[8] Sacker, R. J., A new approach to the perturbation theory of invariant surfaces, Commun Pure Appl. Math., 18, 717-732 (1965) · Zbl 0133.35501
[9] Kelley, A., On the Liapounov subcenter manifold, J. Math. Anal. Appl., 18, 472-478 (1967) · Zbl 0155.14103
[10] LaVita, J.in; LaVita, J.in
[11] Liapounov, A., Probleme General de la Stabilite du Mouvement, (Annals of Mathematical Studies, Vol. 17 (1949), Princeton University Press: Princeton University Press Princeton, New Jersey), 375-392
[12] Siegel, C. L., Vorlesungen uber Himmelsmechanik, ((1956), Springer: Springer Berlin), 82-92 · Zbl 0098.23601
[13] Lykova, O., On the question of stability of solutions of systems of nonlinear differential equations, Ukrain. Mat. Zh., 11, 251-255 (1959), (in Russian) · Zbl 0087.29702
[14] Lykova, O., Investigation of the solutions of nonlinear systems close to integrable systems by using the method of integral manifolds, (Proceedings of the International Symposium on Nonlinear Oscillations, Vol. I (1963), Akademii Nauk U.S.S.R: Akademii Nauk U.S.S.R Kiev), 315-323, (in Russian) · Zbl 0207.38903
[15] Chen, K. T.; Chen, K. T.
[16] Pliss, V. A., Principal reduction in the theory of the stability of motion, Izv. Akad. Nauk · Zbl 0131.31505
[17] Kelley, A., The center manifold and integral manifolds for Hamiltonian systems, Notices Am. Math. Soc., 12, 143-144 (1965)
[18] Kelley, A., Stability of the center-stable manifold, J. Math. Anal. Appl., 18, 336-344 (1967) · Zbl 0166.08304
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