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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:

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[4] Hale, J, On the method of Krylov-Bogoliubov-mitropolski for the existence of integral manifolds of perturbed differential systems, (), 51-57 · Zbl 0121.07403
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[10] {\scLaVita, J.}, Concerning a theorem of Liapounov, in “Hamiltonian Systems,” pp. 202-211 (unpublished notes collected by J. Moser).
[11] Liapounov, A, Probleme general de la stabilite du mouvement, (), 375-392
[12] Siegel, C.L, Vorlesungen uber himmelsmechanik, (), 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, (), 315-323, (in Russian)
[15] {\scChen, K. T.}, On nonelementary hyperbolic fixed points of diffeomorphisms (unpublished).
[16] Pliss, V.A, Principal reduction in the theory of the stability of motion, izv. akad. nauk S.S.S.R., mat ser., 28, 1297-1324, (1964), (in Russian) · 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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